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Mesons in gauge/gravity duals
Abstract
We review recent progress in studying mesons within gauge/gravity duality, in the context of adding flavour degrees of freedom
to generalizations of the AdS/CFT correspondence. Our main focus is on the “top-down approach” of considering models constructed
within string theory. We explain the string-theoretical constructions in detail, aiming at non-specialists. These give rise
to a new way of describing strongly coupled confining large-N gauge theories similar to large-N QCD. In particular, we consider gravity dual descriptions of spontaneous chiral symmetry breaking, and compare with lattice
results. A further topic covered is the behaviour of flavour bound states in finite-temperature field theories dual to a gravity
background involving a black hole. We also describe the “bottom up” phenomenological approach to mesons within AdS/QCD. Some
previously unpublished results are also included.
... From this anomalous dimension, we obtain the glueball masses M i shown in the second column of Table III with the corresponding errors given by Eq. (38), together with the deviations δ i ¼ jM latt − M i j=M latt from average lattice data (Table I) and the effective anomalous dimensions of the glueball operators J þþ . In Fig. 1, we present the Regge trajectory, which is built up as a linearization of these glueball masses, reproducing the soft pomeron trajectory, J ¼ 1.08 AE 0.21 þ ð0.25 AE 0.01ÞM 2 with χ 2 =ndf ¼ 3.76=3 ¼ 1. 25. ...
... Masses in GeV of the J þþ glueball operators from J ¼ 0 to J ¼ 10 for the logarithm anomalous HW models (HW log 1 ) and (HW log 2 ) defined by Eq. (29) with the logarithm contributions to the anomalous dimensions Eqs. (46) and (47), respectively, with errors calculated according to Eq. (38). The orders ν of the corresponding Bessel functions are shown for each glueball state for the two models. ...
... We also show the relative deviations δ log 1;2 compared with lattice data, and the corresponding anomalous dimensions Δ log 1;2 anom ≡ Δ log 1;2 − ð4 þ SÞ of the states J þþ in this model. Table III with the corresponding errors given by Eq. (38), together with the deviations with respect to average lattice data and the corresponding anomalous dimensions of the states J þþ in this model. Third, we consider the AHWlog model with 0 ≤ S ≤ 10 and S 0 ¼ 4, so that the states 0 þþ , 2 þþ , and 4 þþ have canonical conformal dimensions, whilst higher spins follow Eq. ...
In this work we propose improved holographic hard wall (HW) models by the inclusion of anomalous dimensions in the dual operators that describe glueballs inspired by the AdS/CFT correspondence. The anomalous dimensions come from well known semiclassical gauge/string duality analysis showing a dependence with the logarithm of spin S of the boundary states. We show that these logarithm anomalous dimensions of the high spin operators combined with the usual HW model allow us to match the pomeron trajectory and give glueball masses that are better than that of the original HW and soft wall models in comparison with lattice data. We also build up other anomalous HW models considering that the logarithm anomalous dimensions can be approximated by a truncated series of odd powers of the difference S−1/S. These models also fit the pomeron trajectory and produce good glueball masses. Then, we consider an anomalous dimension that is proportional to S, providing reasonable results. Finally, we propose an asymptotic linear anomalous HW model that effective dimensions for high spins operators are of the form Δ=aS+b, where a and b are constants to be fixed by comparison with the soft pomeron trajectory. In this last model, the Regge trajectory is asymptotically linear even for very high spins (J∼100) matching the soft pomeron trajectory accurately and generates glueball masses with deviations with respect to the lattice data better than the original HW and soft wall models.
... These hadrons arise from the lowest energy normalizable modes in the bulk. The justification for these models is provided by the Dirac-Born-Infeld (DBI) action of probe branes in top-down models, such as the Sakai-Sugimoto model [5] or the D3/probe D7 system [6][7][8]. ...
... The dimension of each quark inqq has fallen to one at the hard wall in order to trigger chiral symmetry breaking. By (8), the dimension of a three-quark operator should therefore have fallen to Δ ¼ 3 in the IR, i.e., m 2 eff ¼ 6. If one just uses this lower bulk mass over the full range of r, then the predicted baryon mass falls to ...
... The model, analogous to some of the earliest hard-wall models, attempts to make the minimum number of changes to a basic AdS/QCD model that will exemplify the physics under discussion without it being a first principle holographic description of QCD. Mostly, we import insights from the D3/probe D7 system [6][7][8]. ...
In holographic models of quantum chromodynamics, the running of the anomalous dimension of the quark bilinear operator leads to chiral symmetry breaking when γ=1 and the Breitenlohner-Freedman bound is violated. In that case, the running drives the sigma meson mass tachyonic inducing the chiral symmetry breaking. Here we include the running anomalous dimension in the computation of the spectrum of bound states associated with other operators made of light quarks, such as the nucleon and exotic sexaquark states. We show that including the one-loop gauge theory running can have substantial effects on the predictions. For example, the nucleon mass to rho mass ratio is improved and lies much closer to the observed value. A similar result is obtained for the Λ and Ξ baryon when strange quarks are included. A uuddss sexaquark state with a low enough mass to make it stable can be achieved, but this depends on the input assumptions about the running dimension.
... Gauge/gravity duality concepts were applied to QCD-like theories to address chiral symmetry breaking for instance in [3,4,8]. Meson masses were calculated in the approach in [9][10][11]21], and baryon masses in [5,12]. These approaches provide sensible predictions for the meson spectrum and couplings, at least at the 15% level, or even better [12][13][14]21,22]. ...
... Meson masses were calculated in the approach in [9][10][11]21], and baryon masses in [5,12]. These approaches provide sensible predictions for the meson spectrum and couplings, at least at the 15% level, or even better [12][13][14]21,22]. Moreover, the results compare favourably to lattice studies [12][13][14]21,22]. ...
... These approaches provide sensible predictions for the meson spectrum and couplings, at least at the 15% level, or even better [12][13][14]21,22]. Moreover, the results compare favourably to lattice studies [12][13][14]21,22]. ...
We investigate a holographic model for both spontaneous and explicit symmetry breaking of non-abelian flavour symmetries. This consists of a bottom-up model inspired by the top-down D3/probe D7-brane model. It incorporates the running anomalous dimensions of the fields. We ensure that in the holographic bulk, the full non-abelian flavour symmetries for massless quarks are present. The quark masses are spontaneously generated field values in the bulk and there is a resultant bulk Higgs mechanism. We provide a numerical technique to find the mass eigenvalues from a system of mixed holographic fields, testing it against an analytic model of N=2 supersymmetric matter fields. We apply these ideas to two-flavour QCD with both u−d quark mass splitting and multi-trace bulk action terms that are expected to break U(Nf)V to SU(Nf)V×U(1)V away from large N. We also discuss three-flavour QCD with strange quark mass splitting and applications to more exotic symmetry breaking patterns of potential relevance for composite Higgs models.
... An intensive research effort has been devoted to this task. For a review of this direction see [8]. It is probably fair to state that, apart from one exception, the outcome spectra do not fit well the experimental data. ...
... This idea was further explored in [51] and in many other followup works. For a list of them see the review [8]. There have been certain attempts to go beyond the flavor probe approximation for instance [52]. ...
... which holds for any integer k. 8 Let us look more closely at the resulting amplitude (4.29), for even ∆. Substituting (4.31) yields ...
A bstract
We study the emergence of partonic behavior in scattering processes at large Mandelstam’s variable s from string amplitudes in holographic backgrounds. We generalize the approach of Polchinski and Strassler [1] in two ways. (i) We analyze several holographic confining backgrounds, in particular the hard wall model, the soft wall model and Witten’s model. (ii) In addition to deriving the asymptotic behavior of the amplitudes at fixed angle and in the Regge limit, we also expand the amplitudes around their poles, integrate over the holographic direction and then re-sum the expansion. Due to dependence of the string tension on the holographic coordinate, the resulting singularities take the form of branch points rather than poles and the amplitudes display branch cuts and acquire a finite imaginary part. This may signal the failure of the PS prescription to reproduce the correct analytic structure at low energies. We also observe that the peaks are more pronounced in the region of small s but fade away for large s . In the fixed angle approximation we find in the hard and soft wall models that $$ \mathcal{A} $$ A ∼ s 2 − ∆ / 2 whereas in Witten’s model $$ \mathcal{A} $$ A ∼ s 3 − ∆ / 2 and $$ \mathcal{A} $$ A ∼ s 7 / 3 − 2∆ / 3 for the 11D and 10D formulations, respectively. In the Regge regime $$ \mathcal{A} $$ A ∼ s ² t − 2+ α (log s/t ) − 1+ α where α is the power found in the fixed angle regime. Using the pole expansion the result for each model is Re [ $$ \mathcal{A} $$ A ] ∼ s − 1 , Im [ $$ \mathcal{A} $$ A ] ∼ s α . We compute the corresponding amplitudes for mesons using open strings and find qualitatively similar results as for closed strings.
... An intensive research effort has been devoted to this task. For a review of this direction see [8]. It is probably fair to state that, apart from one exception, the outcome spectra do not fit well the experimental data. ...
... This idea was further explored in [49] and in many other followup works. For a list of them see the review [8]. There have been certain attempts to go beyond the flavor probe approximation for instance [50]. ...
... which holds for any integer k. 8 Let us look more closely at the resulting amplitude 4.29, for even ∆. Substituting 4.31 yields ...
We study the emergence of partonic behaviour in scattering processes at large Mandelstam's variable $s$ from string amplitudes in holographic backgrounds. We generalize the approach of Polchinski and Strassler (2001) in two ways. (i) We analyze several holographic confining backgrounds in particular the hard wall model, the soft wall model and Witten's model. (ii) In addition to deriving the asymptotic behavior of the amplitude at fixed angle and in the Regge limit, we also expand the amplitudes around their poles, integrate over the holographic direction and then re-sum the expansion. Due to dependence of the string tension on the holographic coordinate, the resulting singularities take the form of branch points rather than poles and the amplitudes display branch cuts and acquire a finite imaginary part. This may signal the failure of the PS prescription to reproduce the correct analytic structure at low energies. We also observe that the peaks are more pronounced in the region of small $s$ but fade away for large $s$. In the fixed angle approximation we find in the hard and soft wall models that ${\cal A}\sim s^{2-\Delta/2}$ whereas in Witten's model ${\cal A} \sim s^{3-\Delta/2}$ and ${\cal A} \sim s^{7/3-2\Delta/3}$ for the 11D and 10D formulations, respectively. In the Regge regime ${\cal A}\sim {s^{2}}\,t^{-2+\alpha}\,(\log{s/ t})^{-1+\alpha}$ where $\alpha$ is the power found in the fixed angle regime. Using the pole expansion the result for each model is $Re[{\cal A}] \sim s^{-1}$, $Im[{\cal A}] \sim s^{\alpha}$. We compute the corresponding amplitudes for mesons using open strings and find qualitatively similar results as for closed strings.
... In this paper, we consider N f = 1 for simplicity. The spectrum of mesons, namely quark-antiquark bound states, in the N = 2 theory has been intensively explored by considering the fluctuations of the D7-brane [5] (see review [6] and references therein). A natural question to ask is how the meson spectrum will change in the presence of an external electric/magnetic field. ...
... At zero electric field in the vacuum, the embedding of the probe D7-brane is exactly given byW (u) = sin θ(u)/u = m. Moreover, every linear perturbation on the D7-brane, 6 More precisely, the actual Green's function G R (ω) in the dual field theory is given by Here, χ ± are the coupled modes of the scalar and vector parallel to E, denoted by n ± . Note that they are given by χ ± = w ± ia ∥ at first order in E. In large E limit, equivalently massless limit, they are decoupled again and we can identify the scalar w and vector a ∥ , respectively. ...
A bstract
We study the meson spectrum of the $$ \mathcal{N} $$ N = 4 supersymmetric Yang-Mills theory with $$ \mathcal{N} $$ N = 2 fundamental hypermultiplets for a finite electric field by using the D3/D7 model. The spectrum for scalar and vector mesons is computed by analyzing the (quasi-)normal modes for the fluctuations of the D7-brane embedding and gauge fields. In the presence of an electric field, two different phases in the background are realized: the meson and dissociation phases. In this paper, we analyze the meson spectrum of scalar and vector mesons for all ranges of the electric field and explore the effect of the electric field on the meson spectrum, that is, the Stark effect. In the meson spectrum, we observe the avoided crossing between different levels due to the coupling of fluctuations via the electric field.
... By mapping a d-dimensional strong coupling theory to a (d þ 1)dimensional asymptotically anti-de Sitter (AdS) spacetime, one can instead deal with generic gravitational phenomena in terms of classical general relativity. This holographic approach has been used to study various strongly coupled systems, such as quark-gluon plasma [5][6][7][8][9], high temperature superconductivity [10][11][12][13][14], strange metals [15][16][17][18][19], and Fermi/non-Fermi liquids [20,21] and so on. ...
... The basic holographic dictionary requires that the external source φ ðsÞ i contributes to the partition function according to Eq. (3). The first-order derivative of Z QFT with respect to the source gives Eq. (6). What will one obtain if considering the second-order derivative? ...
For a strongly coupled system that has a gravity dual description, we show that the standard holographic dictionary yields a non-negative susceptibility when the system is in thermodynamic equilibrium and the correlation function is absolutely integrable. When the system has no spontaneous condensation or has a spontaneous Z2-symmetry breaking, we find that the “trace energy condition” is violated in many cases. There is a normalized grand potential density that is monotonic as accessing to lower scales, providing a candidate c-function characterizing the number of effective degrees of freedom. Finally, we discuss a “paradox” raising by the negative susceptibility in holography and its resolution.
... String-Inspired Warped Throats -Attempts to UV-complete the RS-like models in string theory exist, e.g. with warped throat geometries à la Klebanov-Strassler [212], but it remains very challenging to find a fully realistic construction [213][214][215]*. Note that in such string theory models, the geometry near the IR-tip of the throat in not AdS 5 , but this does not spoil the RS-mechanism of warp transmutation of scales. ...
... Moreover, as argued in Ref.[17], these spurious poles are in the UV-opaque regime, where microcausality is meaningless, such that one should use an Euclidean prescription for spacetime where ghost-like poles are harmless.19 Remember that warped throat solutions are expected to exist in string theory[213][214][215]*. ...
Particle physics models with extra dimensions of space (EDS's) and branes allow to shed new light on naturalness of the electroweak and flavor sectors, with a rich TeV scale phenomenology. Usually, such models are formulated in the framework of local effective field theories. The scope of this article is to propose new model building issues with EDS and branes, arising in the framework of string-inspired infinite derivative quantum field theories (QFT's), which are perturbatively exorcized (ghost-free) and intrinsically nonlocal above some ultraviolet (UV) scale. First, a toy model with bulk and brane scalar fields is presented. It is shown that a 4D field localized on a $\delta$-like 3-brane is still delocalized in the bulk on a small distance from the brane position, with a penetration length given by the nonlocal length scale. Fields localized on such distant fuzzy branes are thus allowed to interact directly with suppressed couplings, which is impossible in a local QFT. It is also argued that above the nonlocal scale, it should be much more difficult to probe the Kaluza-Klein (KK) tower in an experiment, because of the UV opaqueness of such infinite derivative QFT's. In this way, a shadow EDS is obtained if the nonlocal and KK scales are close to each other, such that the effects of the KK-excitations are screened compared to a local QFT. After that, directions for model building are given. By using this new possibility of fuzzy branes, a new realization of split fermions in an EDS is presented, allowing to naturally generate flavor hierarchies. Moreover, with a warped EDS, the usual warp transmutation of a brane mass term is revisited, where it is shown that the nonlocal scale is also redshifted. This may provide a new way to solve or reduce the little hierarchy problem related to the Higgs boson mass.
... As a first step in this direction, we consider spatially dependent masses in the D3/probe D7 system which is a very well understood holographic construction [3,4]. The base D3/probe D7 system describes an N ¼ 2 quark hypermultiplet in the fundamental representation interacting with the adjoint fields of N ¼ 4 super Yang Mills theory. ...
... A supersymmetry preserving, x-independent mass can be included by the solution u 1 ¼ m with m q ¼ m=2πα 0 . The meson spectrum for this case has been computed in [4]. ...
We study domain wall fermions and their condensation in the D3/probe D7 system. A spatially dependent mass term for the N=2 hypermultiplet can be arranged to isolate distinct two-component fermions on two 2+1 dimensional domain walls. We argue that the system shows condensation/mass generation analogous to the D3/probe D5 D5¯ system. The chiral condensate and pion mass can be directly computed on the domain wall. We provide evidence that these systems with the domains separated by a width w have a bare (current) quark mass that scales as 1/w when the spatially dependent mass is large. Adding a magnetic field does not induce chiral symmetry breaking between the separated domain wall fermions, but a similar phenomenological dilaton factor can be made strong enough to introduce spontaneous symmetry breaking. We show a Gell-Man-Oakes-Renner relation for the pions in that case and also for the case where the D7 probe is in a backreacted dilaton flow geometry. The vacuum configurations can also be interpreted as having a spontaneously generated mass by a Nambu-Jona-Lasinio four fermion operator, depending on the choice of boundary conditions on fluctuations, according to Witten’s multitrace prescription.
... The study of the holographic transition between confining and deconfined phases and of plasma balls was presented in many other publications. In addition to the ones mentioned earlier, a partial list includes [23][24][25][26][27][28] and references therein, [29][30][31][32][33][34][35][36][37][38][39][40][41]. Recently, applications of holography to first order phase transitions in the early universe and to the production of gravitational waves has received a lot of attention [42][43][44][45]. ...
... In this work we will be interested mainly in the latter but our conclusions will apply also to the former scenarios. Several different gravitational backgrounds that are confining backgrounds were written down (for a review see [28] and references therein). It is well known that the gravitational duals of deconfined systems take the form of black-hole backgrounds. ...
A bstract
In the context of theories with a first order phase transition, we propose a general covariant description of coexisting phases separated by domain walls using an additional order parameter-like degree of freedom. In the case of a holographic Witten model with a confining and deconfined phase, the resulting model extends hydrodynamics and has a simple formulation in terms of a spacetime action with corresponding expressions for the energy-momentum tensor. The proposed description leads to simple analytic profiles of domain walls, including expressions for surface tension density, which agree nicely with holographic numerical solutions, despite the apparent complexity of those gravitational backgrounds.
... Revs. [202][203][204]). Note that in such superstring models, the geometry near the IR-tip of the throat in not AdS 5 , but this does not spoil the RS mechanism of warp transmutation of scales. ...
... Nonlocality should thus give only corrections to the standard background one has in local warped models like RS1[206,207]. Moreover, because warped throats exist in string theory[201][202][203][204], which is a serous possibility of nonlocal UV completion, this assumption appears as well justified.14 "GF" is for "ghost-free".15 ...
Particle physics models with extra dimensions of space (EDS's) and branes are very interesting extensions beyond the standard model (BSM), allowing to shed new light on electroweak and flavor naturalness. Usually, such models are formulated in the framework of local effective field theories (EFT's). The scope of this article is to propose new model building issues in BSM constructions with EDS and branes, arising in the framework of exorcized (ghost-free) infinite derivative field theories (IDFT's), which are intrinsically nonlocal above some ultraviolet (UV) scale Λ_NL. First, with a warped EDS, the warp transmutation of the mass term of a brane-localized scalar field is revisited, where it is shown that Λ_NL is also redshifted. This may provide a new way to solve the little hierarchy problem related to the Higgs boson mass. Moreover, if the (redshifted) Λ_NL is around the mass scale of the first Kaluza-Klein (KK) excitations of the bulk fields, it is argued that it would be much more difficult to probe the KK tower in an experiment, which is reminiscent to the UV opaqueness of IDFT's: such EDS is then dubbed shadow. After that, it is shown that a 4D field localized on a δ-like 3-brane is still delocalized in the bulk on a distance O(1/Λ_NL) of the brane position, such as 2 fields localized on 2 different δ-like branes are allowed to interact with suppressed couplings, which is impossible in a local EFT. By using this new possibility of fuzzy branes, a new realization of the split fermion idea is presented, allowing to build new BSM models of flavor.
... The CEP has been extensively investigated in four-dimensional effective QCD models, e.g., the Nambu-Jona-Lasinio, linear sigma model [14,15], and their Polyakov-loop extended version [16][17][18][19], the Dyson-Schwinger equations (DSEs) [20][21][22][23], and the functional renormalization group (FRG) [24,25]. In recent decades, the holographic gauge-gravity duality [26] has been widely applied as an important nonperturbative method in describing hadron physics [27][28][29][30] and QCD matter under extreme conditions [31][32][33][34][35][36][37][38][39][40][41][42][43][44][45][46][47][48]. The fivedimensional Einstein-Maxwell-Dilaton (EMD) framework [34][35][36][37][38][39][45][46][47][48] has been adapted as the working framework for describing QCD matter at finite temperature and density. ...
Based on lattice QCD results of equation of state and baryon number susceptibility at zero baryon chemical potential, and supplemented by machine learning techniques, we construct the analytic form of the holographic black hole metric in the Einstein-Maxwell-Dilaton framework for pure gluon, 2-flavor, and (2+1)-flavor systems, respectively. The dilaton potentials solved from Einstein equations are in good agreement with the extended nonconformal DeWolfe-Gubser-Rosen type dilaton potentials fixed by lattice QCD equation of state, which indicates the robustness of the Einstein-Maxwell-Dilaton framework. The predicted critical end point in the (2+1)-flavor system is located at (Tc=0.094 GeV, μBc=0.74 GeV), which is close to the results from the realistic Polyakov-Nambu-Jona-Lasinio model, the functional renormalization group, and the holographic model with extended DeWolfe-Gubser-Rosen dilaton potential.
... One famous example of these models is known as the Witten-Sakai-Sugimoto model [77][78][79], which can be constructed from string theory. Such models can also be built from low-energy EFTs of gauge fields with gravitational couplings [110][111][112][113][114][115][116], where the fits to the experimental data of hadrons, glueballs, and so on have been extensively studied (see e.g., [117,118] for brief reviews). Typically, at low energy, the holographic models can also give rise to the χPT Lagrangian with Wilson coefficients mapping to parameters on the gravity side [78,79,[111][112][113][114][115][116]. ...
A bstract
We review the effective field theory (EFT) bootstrap by formulating it as an infinite-dimensional semidefinite program (SDP), built from the crossing symmetric sum rules and the S-matrix primal ansatz. We apply the program to study the large- N chiral perturbation theory ( χ PT) and observe excellent convergence of EFT bounds between the dual (rule-out) and primal (rule-in) methods. This convergence aligns with the predictions of duality theory in SDP, enabling us to analyze the bound states and resonances in the ultra-violet (UV) spectrum. Furthermore, we incorporate the upper bound of unitarity to uniformly constrain the EFT space from the UV scale M using the primal method, thereby confirming the consistency of the large- N expansion. In the end, we translate the large- N χ PT bounds to constrain the higher derivative corrections of holographic QCD models.
... The discovery of the anti-de Sitter/conformal field theory (AdS/CFT) correspondence [40][41][42] has provided a new way to solve strongly coupled field theory calculations. In the past two decades, holographic QCD has been widely studied both in top-down [43][44][45] and bottom-up models [46][47][48][49][50][51][52]. For beyond the standard model the technicolor model [53][54][55][56][57][58] and composite Higgs model [59][60][61][62] have been extended to the holographic framework. ...
A bstract
We investigate the bounce solution in the holographic dark-QCD and electroweak models with first-order phase transition. The strength parameter α , inverse duration time β / H and bubble wall velocity v w in the gravitational wave power spectra are calculated by holographic bounce solution. We find the parameter α is about 𝒪(1) and β / H is about 10 ⁴ , which implies that the phase transition is fast and strong. The critical temperature, nucleation temperature and the temperature at the beginning time of the phase transition are close to each other in the holographic model. In addition, the velocity v w is found to be less than the sound speed of the plasma $$ {c}_s=1/\sqrt{3} $$ c s = 1 / 3 , which corresponds to the deflagration scenario. The gravitational wave signal from phase transitions is difficult to detect since the factor ϒ suppresses the gravitational wave power spectrum. The GW signal can be detected only when the model is in the period of electroweak phase transition and with suitable parameters. Moreover, the primordial black hole is not favorable for formation due to the large parameter β / H and small velocity v w .
... The spectrum of mesons, namely quark-antiquark bound states, in the N = 2 theory has been intensively explored by considering the fluctuations of the D7-brane [5] (see review [6] and references therein). A natural question to ask is how the meson spectrum will change in the presence of an external electric/magnetic field. ...
We study the meson spectrum of the ${\cal{N}}=4$ supersymmetric Yang-Mills theory with ${\cal{N}}=2$ fundamental hypermultiplets for a finite electric field by using the D3/D7 model. The spectrum for scalar and vector mesons is computed by analyzing the (quasi-)normal modes for the fluctuations of the D7-brane embedding and gauge fields. In the presence of an electric field, two different phases in the background are realized: the meson and dissociation phases. In this paper, we analyze the meson spectrum of scalar and vector mesons for all ranges of the electric field and explore the effect of the electric field on the meson spectrum, that is, the Stark effect. In the meson spectrum, we observe the avoided crossing between different levels due to the coupling of fluctuations via the electric field.
... Within string theory and supergravity, it has been discovered that gauge-gravity dualities, or holography [80][81][82][83], provide an alternative way to study special field theories in their nonperturbative regime. Applications include the holographic description of confinement [84][85][86][87], the study of the composite (glueball) mass spectra [88][89][90][91][92][93][94][95][96][97][98][99], chiral symmetry breaking [100,101], and masses of mesons [102][103][104][105][106]. But it is very challenging to embed within string theory and supergravity fully realistic dynamical models yielding the low-energy theories relevant to CHMs. ...
We study a bottom-up, holographic description of a field theory yielding the spontaneous breaking of an approximate SO(5) global symmetry to its SO(4) subgroup. The weakly coupled, six-dimensional gravity dual has regular geometry. One of the dimensions is compactified on a circle that shrinks smoothly to zero size at a finite value of the holographic direction, hence introducing a physical scale in a way that mimics the effect of confinement in the dual four-dimensional field theory. We study the spectrum of small fluctuations of the bulk fields carrying SO(5) quantum numbers, which can be interpreted as spin-0 and spin-1 bound states in the dual field theory. This work supplements an earlier publication focused only on the SO(5) singlet states. We explore the parameter space of the theory, paying particular attention to composite states that have the right quantum numbers to be identified as pseudo-Nambu-Goldstone bosons (PNGBs). We find that in this model the PNGBs are generally heavy, with masses of the same order as other bound states, indicating the presence of a sizeable amount of explicit symmetry breaking in the field-theory side. Nevertheless, we also find a qualitatively new, unexpected result. When the dimension of the field-theory operator inducing SO(5) breaking is close to half the space-time dimensionality, there exists a region of parameter space in which the PNGBs and the lightest scalar are both parametrically light in comparison to all other bound states of the field theory. Although this region is known to yield metastable classical backgrounds, this finding might be relevant to model building in the composite Higgs context.
... It is conformal to leading order, as the running of the gauge coupling due to the presence of the hypermultiplets is subleading in 1/N c for N f ∼ O(1). Its associated holographic physics has been analysed in detail, [101,76,77]. Because the embedding of the flavor branes inside AdS 5 × S 5 is non-trivial the flavour gauge fields are subjected to a different open string metric than in the previous items. ...
A (toy) model for cold and luke-warm strongly-coupled nuclear matter at finite baryon density and isospin chemical potential is used to study neutrino transport. The complete charged current two-point correlators are computed in the strongly-coupled medium and their impact on neutrino transport is analyzed. The full result is compared with various approximations for the current correlators and the distributions, including the degenerate approximation, the hydrodynamic approximation as well as the diffusive approximation and we comment on their successes. Further improvements are discussed.
... extra dimension as an emergent energy scale or renormalization group (RG) flow in the QFT [6]. There have been numerous efforts to construct a non-conformal 5-dimensional holographic QCD model via both top-down and bottom-up approaches, for example, the system from top-down, including the [7] and systems, or the Witten-Sakai-Sugimoto (WSS) model [8,9]. ...
The simplest version of the dynamical holographic QCD model is described by adding the KKSS model action on a dilaton-graviton coupled background, in which the AdS_5 metric is deformed by the gluon condensation and further deformed by the chiral condensation. In this framework, both the chiral symmetry breaking and linear confinement can be realized, the light-flavor hadron spectra and the pion form factor were investigated but it was difficult to reconcile the light-flavor hadron spectra and pion form factor. By considering the anomalous 5-dimension mass correction of the scalar field from QCD running coupling, it is found that the light flavor hadron spectra and pion form factor can be described well simultaneously, especially the ground state and lower excitation states of scalar, pseudo scalar and axial vector meson spectra are improved, but the vector meson spectra is not sensitive to the anomalous 5-dimension mass correction of the scalar field.
... There have been lots of efforts to construct a non-conformal 5-dimensional holographic QCD model from both top-down and bottom-up. For example, the D p − D q system from top-down including the D 3 − D 7 [7] and the D 4 − D 8 system or the Witten-Sakai-Sugimoto (WSS) model [8,9]. In the bottom-up approach, the hard-wall model [10] and soft-wall AdS/QCD model or KKSS model [11] established the 5-dimensional framework for light hadron spectra. ...
The simplest version of the dynamical holographic QCD model is described by adding the KKSS model action on a dilaton-graviton coupled background, in which the AdS$_5$ metric is deformed by the gluon condensation and further deformed by the chiral condensation. In this framework, both the chiral symmetry breaking and linear confinement can be realized, the light-flavor hadron spectra and the pion form factor were investigated but it was difficult to reconcile the light-flavor hadron spectra and pion form factor. By considering the anomalous 5-dimension mass correction of the scalar field from QCD running coupling, it is found that the light flavor hadron spectra and pion form factor can be described well simultaneously, especially the ground state and lower excitation states of scalar, pseudo scalar and axial vector meson spectra are improved, but the vector meson spectra is not sensitive to the anomalous 5-dimension mass correction of the scalar field.
... The curve interpolates between two endpoints. On one end, |j| = 0, and we find the frequencies corresponding exactly to the vector meson masses i.e. the fluctuations in the probe brane worldvolume gauge field [21]. We have checked this in appendix F (see figure 13 for the first three meson masses). ...
A bstract
We continue the study in [1] of a strongly coupled (2+1)-dimensional gauge theory subject to an external rotating electric field. The system is modelled holographically as a D3/D5 probe intersection. We add temperature to the D3 background and analyze the phase diagram. Also here, the conductive phase extends down to vanishing external electric field at discrete values of the frequencies where vector meson Floquet condensates form. For all temperatures, at given intercalated frequencies, we find new dual states that we name Floquet suppression points where the vacuum polarization vanishes even in the presence of an electric field. From the data we infer that these states exist both in the conductive and insulating phases. In the massless limit we find a linear and instantaneous conductivity law, recovering known general results in 2+1 dimensions. We also examine the photovoltaic AC and DC current as the response to an oscillating probe electric field and see that rising the temperature suppresses the photovoltaic Hall current. All the results obtained carry over qualitatively unaltered to the case of D3/D7.
... According to the holographic principle, a D-dimensional field theory is dual to the (D þ 1)-dimensional gravitational theory, and the extra dimensions can be understood as renormalization group flows [56]. Starting from string theory, various top-down models, such as the D 3 − D 7 model [57], the Witten-Sakai-Sugimoto model [58,59], and the STU model [60][61][62] have been widely studied to detect the properties of strongly coupled theories. Another method known as bottom-up approach, such as the hard-wall model [63,64], the softwall model [65], the Gubser model [66][67][68][69], the improved holographic QCD model [70][71][72], the refined model [73], the Dudal model [74], and the dynamical holographic QCD model (DhQCD) [75][76][77][78] have extensively studied hadron spectra, thermodynamic and transport properties of QCD matter, and QCD phase transitions. ...
We investigate inhomogeneous chiral condensation under rotation considering finite size effects and boundary conditions in the holographic QCD model. The rotational suppression effect determined by Ωr is confirmed in the holographic model which is not influenced by the boundary conditions. For chiral condensation at the center, it is found that under Neumann boundary condition the finite size exhibits two opposite effects, i.e., catalysis at high temperatures and inverse catalysis at low temperatures. In contrast, under Dirichlet boundary condition, the effect of finite size on condensation is inverse catalysis, and small size induces a phase transition from inhomogeneous to homogeneous phase. The temperature-angular velocity phase diagrams of QCD are obtained for different boundary conditions and sizes, and it is found that the critical temperature decreases with angular velocity.
... The curve interpolates between two endpoints. On one end, |j| = 0, and we find the frequencies corresponding exactly to the vector meson masses i.e. the fluctuations in the probe brane worldvolume gauge field [21]. We have checked this in Appendix F (see Fig. 13 for the first three meson masses). ...
We continue the study in [1] of a strongly coupled (2+1)-dimensional gauge theory subject to an external rotating electric field. The system is modelled holographically as a D3/D5 probe intersection. We add temperature to the D3 background and analyze the phase diagram. Also here, the conductive phase extends down to vanishing external electric field at discrete values of the frequencies where vector meson Floquet condensates form. For all temperatures, at given intercalated frequencies, we find new dual states that we name Floquet suppression points, where the vacuum polarization vanishes even in the presence of an electric field. From the data we infer that these states exist both in the conductive and insulating phases. In the massless limit we find a linear and instantaneous conductivity law, recovering known general results in 2+1 dimensions. We also examine the photovoltaic AC and DC current as the response to an oscillating probe electric field and see that rising the temperature suppresses the photovoltaic Hall current. All the results obtained carry over qualitatively unaltered to the case of D3/D7.
... If we consider a theory with a number of color degrees of freedom, N c , and a number, N f , of flavors then the quenched limit corresponds to N f Nc → 0. There are many interesting results in this limit, such as meson spectroscopy [11][12][13][14][15], the description of chiral symmetry breaking [16,17] or field theories furnishing spatial defects of different dimensionalities [18,19]. We refer the interested reader to [20,21] for more discussion and a detailed account of some of these developments. ...
A bstract
We construct gravity duals to supersymmetric gauge theories in the presence of unquenched flavor hypermultiplets in the fundamental representation of the gauge group living on the (1+1)-dimensional defect. This configuration is given by the intersection of two sets of D3-branes. Working in the Veneziano limit with large number of colors and flavors we are able to find a closed set of equations describing the dual geometry. We briefly discuss the corresponding solutions for massless flavors as well as in the small flavor limit of massive hypermultiplets. Interestingly, the $$ \frac{1}{16} $$ 1 16 -BPS supergravity solutions, preserving two Poincaré supercharges, are generically only asymptotically anti de-Sitter and the dilaton does not vary with the holographic radial coordinate. This implies that the classical Type IIB supergravity solutions remain trustworthy descriptions for the gauge theories from the deep IR to the far UV.
... According to the holographic principle, a D-dimensional field theory is dual to the (D + 1)-dimensional gravitational theory, and the extra dimensions can be understood as renormalization group flows [53]. Starting from string theory, various topdown models, such as the D 3 − D 7 model [54], the Witten-Sakai-Sugimoto model [55,56], and the STU model [57][58][59] have been widely studied to detect the properties of strongly coupled theories. Another method known as bottomup approach, such as the hard-wall model [60], the soft-wall model [61], the Gubser model [62][63][64][65], the improved holographic QCD model [66][67][68], the refined model [69], the Dudal model [70], and the dynamical holographic QCD model (DhQCD) [71][72][73][74] have extensively studied hadron spectra, thermodynamic and transport properties of QCD matter, and QCD phase transitions. ...
We investigate inhomogeneous chiral condensation under rotation considering finite size effects and boundary conditions in the holographic QCD model. The rotational suppression effect determined by $\Omega r$ is confirmed in the holographic model which is not influenced by the boundary conditions. For chiral condensation at the center, it is found that under Neumann boundary condition the finite size exhibits two opposite effects, i.e., catalysis at high temperatures and inverse catalysis at low temperatures. In contrast, under Dirichlet boundary condition, the effect of finite size on condensation is inverse catalysis, and small size induces a phase transition from inhomogeneous to homogeneous phase. The temperature-angular velocity phase diagrams of QCD are obtained for different boundary conditions and sizes, and it is found that the critical temperature decreases with angular velocity.
... Perturbative QCD can be only applied at very large energies and/or temperatures [KMT01; AM05; MP08]. The AdS/CFT duality has also been used to describe some features of the spectral function, but a clear correspondence with QCD allowing quantitative studies is still missing [Erd+08;Cas+14]. ...
This dissertation investigates exotic hadrons with heavy-quark content that may be understood as being generated dynamically from the hadron-hadron interaction. This interaction is derived from a suitable effective Lagrangian and properly unitarized in a full coupled-channel basis. In particular, we discuss the possible interpretation of some of the {\Omega}c* excited states recently discovered at LHCb as being meson-baryon molecular states. We also discuss the dynamical generation of excited open-charm mesons from the scattering of pseudoscalar and vector charmed mesons off light mesons. We show that a double-pole structure is predicted for the D0*(2300) state, as well as for the D1(2430), while the Ds0*(2317) and the Ds1(2460) may be interpreted as molecular bound states. Extensions of these calculations to the bottom sector are also presented. Furthermore, we investigate the thermal modification of the open heavy-flavor mesons in a hot medium. By means of an extension to finite temperature of the unitarized effective interactions with the light mesons, we obtain the in-medium spectral properties of the D, D*, Ds, and Ds* ground-state mesons. We also analyze the temperature dependence of the masses and the decay widths of the dynamically generated states. Additionally, we provide results for the bottomed mesons by exploiting the heavy-quark spin-flavor symmetry of the Lagrangian. We employ the temperature-dependent spectral functions to compute charm Euclidean correlators. We also present calculations of off-shell transport coefficients in the hadronic phase implementing in-medium scattering amplitudes and the thermal dependence of the heavy-meson spectral properties.
... For instance, these models do not have fundamental degrees of freedom ab initio. They should be added by geometrical deformations, such as another stack of D-branes, whose Chan-Paton charge corresponds with the number of flavors of theory [2]. ...
This work discusses the electromagnetic (EM) pion form factor ($\pi FF$) in a deformed AdS geometry. We consider the conformal dimension of the hadron bulk field defined by the scaling dimension of the $q\,\bar{q}$ operator instead of the twist. We also compute the pion EM radius and compare it with the experimental data, finding a relative error of $2\,\%$.
... Being top-down, our model has the attractive feature that the Lagrangian is known: see for example refs. [119,120] for explicit expressions. However, its full form is lengthy, so we will write only the terms we need, namely terms in the potential V that involve the complex hypermultiplet mass m e iφ , ...
The gauge/gravity duality links the fields of string theory and quantum field theory. The duality states that systems that are strongly coupled in one theory are weakly coupled in the other. Thus, intractable problems in strongly coupled physics can instead be calculated using the gravity side of the duality. In this thesis we study three areas of strongly coupled physics: quantum chromodynamics, condensed matter theory and (non)-hydrodynamic physics. First, we study quantum chromodynamics (QCD), where we attempt to gain insight into the temperature chemical potential QCD phase diagram by extending an exactly soluble holographic model into imaginary chemical potential. We then look for structure at small real µ and imaginary µ that help to reconstruct the large real µ phase diagram. We find that the phase diagram has boundaries of regions where metastable vacua exist and these boundaries, as well as the phase boundaries, converge at the holographic QCD critical point. We then move on to condensed matter theory where we study a top-down holographic Weyl semi-metal where we find the defining characteristic of a Weyl semi-metal: a quantum phase transition from a topological state with non-zero anomalous Hall conductivity to a trivial insulator. Unlike previous models, we find that the anomalous Hall conductivity is independent of model parameters at zero temperature and is also first order. At non-zero temperature the transition remains first order, and the anomalous Hall conductivity acquires non-trivial dependence on model parameters. Finally, we study the transition between non-hydrodynamic modes and hydrodynamic modes in holographic strange metals, where the microscopic description of the collective excitations is unknown but departs from the standard weakly-coupled Fermi liquid theory. We find that by including translational symmetry breaking the propagating non-hydrodynamic modes are damped, until at sufficiently large symmetry breaking parameters the mode transitions to the purely imaginary diffusive hydrodynamic mode.
... Therefore it is possible to construct a non-conformal 5-dimensional holographic QCD model based on the gauge/gravity duality, and there have been lots of efforts both from top-down and bottom-up approaches. From top-down, the D p − D q system including the D 3 − D 7 [16] and the D 4 − D 8 system or the Witten-Sakai-Sugimoto (SS) model [17,18] have been widely explored. In the bottomup approach, the hard-wall AdS/QCD model [19] and the soft-wall AdS/QCD or KKSS model [20] established the 5-dimensional framework for light hadron spectra. ...
In this paper we present a short overview on the dynamical holographic QCD method for hadron physics and QCD matter. The 5-dimensional dynamical holographic QCD model is constructed in the graviton-dilaton-scalar framework with the dilaton background field $\Phi$ and the scalar field $X$ dual to the gluon condensate and the chiral condensate operator thus can represent the gluodynamics (linear confinement) and chiral dynamics (chiral symmetry breaking), respectively. The dilaton background field and the scalar field are a function of the 5th dimension, which plays the role of the energy scale, in this way, the DhQCD model can resemble the renormalization group from ultraviolet (UV) to infrared (IR). By solving the Einstein equation, the metric structure at IR is automatically deformed by the nonperturbative gluon condensation and chiral condensation in the vacuum. We review the results on the hadron spectra including the glueball spectra, the light/heavy meson spectra, as well as on QCD phase transitions, and thermodynamical as well as transport properties in the framework of the dynamical holographic QCD model.
... Recently, inspired by sophisticated holographic models exhibiting QCD-like properties (such as the Sakai-Sugimoto model [127,128] and its precursors [129][130][131]), new bottomup holographic realisations of CHMs have been developed [132,133]. The same coset structures studied on the lattice are here realised by bulk fields, inspired by the DBI action that describes extended objects probing the curved background (and captures the quenched approximation for matter fields in the large-N limit of the field theory). ...
A bstract
Within the context of top-down holography, we study a one-parameter family of regular background solutions of maximal gauged supergravity in seven dimensions, dimensionally reduced on a 2-torus. The dual, four-dimensional confining field theory realises the global (spontaneous as well as explicit) symmetry breaking pattern SO(5) → SO(4). We compute the complete mass spectrum for the fluctuations of the 128 bosonic degrees of freedom of the five-dimensional gravity theory, which correspond to scalar, pseudoscalar, vector, axial-vector, and tensor bound states of the dual field theory, and includes particles with exotic SO(4) quantum numbers. We confirm the existence of tachyonic instabilities near the boundaries of the parameter space.
We discuss the interplay between explicit and spontaneous symmetry breaking. The SO(5) / SO(4) coset might provide a first step towards the realisation of a calculable framework and ultraviolet completion of minimal composite Higgs models, if the four pseudo-Nambu-Goldstone bosons are identified with the real components of the Higgs doublet in the standard model (SM), and a subgroup of SO(4) with the SU(2) × U(1) SM gauge group. We exhibit an example with an additional localised boundary term that mimics the effect of a weakly-coupled external sector.
... In this work, we are going to investigate the glueball spectra in the framework of holographic QCD, which is based on the gravity/gauge duality, or anti-de Sitter/conformal field theory (AdS=CFT) correspondence [55][56][57]. AdS=CFT correspondence offers a new possibility to tackle the difficulty of strongly coupled gauge theories [58][59][60][61]. Many efforts from both top-down and bottom-up approaches have been paid on examining the nonperturbative properties of QCD [62], e.g., QCD equation of state [63][64][65], phase transitions [66][67][68][69][70][71][72], fluid properties of quark-gluon plasma, meson spectra [72][73][74][75][76][77][78][79][80][81][82][83][84], baryon spectra [85][86][87], as well as the glueball sector . ...
We study the spectra of two-gluon glueballs and three-gluon oddballs and corresponding equation of state in 5-dimensional deformed holographic QCD models in the gravity-dilaton system, where the metric, the dilaton field, and the dilaton potential are self-consistently solved from each other through the Einstein field equations and the equation of motion of the dilaton field. We compare the models by inputting the dilaton field, inputting the deformed metric, and inputting the dilaton potential, and find that with only 2 parameters, the 5-dimensional holographic QCD model predictions on glueballs/oddballs spectra, in general, are in good agreement with lattice results except three oddballs states 0+−, 2+− and 3−−. From the results of glueballs/oddballs spectra at zero temperature and the equation of state at finite temperature, we observe that the model with quadratic dilaton field can simultaneously describe glueballs/oddballs spectra as well as the equation of state of pure gluon system. The model with quadratic AE(z) can describe glueballs/oddballs spectra, but its corresponding equation of state behaves more like Nf=2+1 quark matter, which is consistent with the dimension analysis at ultraviolet (UV) boundary. Our results suggest that the Einstein-Maxwell-dilaton model with the profile ϕ(z)=z2 can be regarded as a candidate of dual theory of pure gluodynamics. Though it is still difficult to find the dual theory of full QCD, the existence of dual theory of pure gluodynamics would be quite encouraging.
... For a review of the top-down approach, see, for instance, Refs. [40][41][42]. ...
We investigate nonlinear extensions of the holographic soft wall model proposed by Karch et al. [Phys. Rev. D 74, 015005 (2006)] including nonminimal couplings in the five-dimensional action. The nonminimal couplings bring a new parameter a0 which controls the transition between spontaneous and explicit symmetry breaking near the limit of massless quarks (the chiral limit). In the physical region (positive quark mass), we show that above a critical value of the parameter a0 the chiral condensate ⟨q¯q⟩ is finite in the chiral limit, signifying spontaneous chiral symmetry breaking. This result is supported by the lightest states arising in the spectrum of the pseudoscalar mesons, which become massless in the chiral limit and are therefore intrepreted as Nambu-Goldstone bosons. Moreover, the decay constants of the pseudoscalar mesons also support this conclusion, as well as the Gell-Mann-Oakes-Renner relation satisfied by the lightest states. We also calculate the spectrum of scalar, vector, and axial-vector mesons with their corresponding decay constants. We describe the evolution of masses and decay constants with the increasing of the quark mass, and for the physical mass, we compare our results against available experimental data. Finally, we do not find instabilities in our model for the physical region (positive quark mass).
... It is using in N = 4 super Yang-Mills theories at large number of colours, N c and maps the computations to the weakly coupled gravitational theories. The quark degrees of freedom has been added in the gauge theories in [7][8][9][10][11] so that one can study wider space of such theories using Ad S/QC D [12,13]. Holographic study of cool baryon density and quark matter [14], possible hadron-quark continuity [15] and quarkyonic matter [16] are such examples of applied holography in dense QCD. ...
We study a bottom-up holographic description of the QCD colour superconducting phase in the presence of higher derivative corrections. We expand this holographic model in the context of Gauss–Bonnet (GB) gravity. The Cooper pair condensate has been investigated in the deconfinement phase for different values of the GB coupling parameter $$\lambda _{G B}$$ λ GB , we observe a change in the value of the critical chemical potential $$\mu _c$$ μ c in comparison to Einstein gravity. We find that $$\mu _c$$ μ c grows as $$\lambda _{G B}$$ λ GB increases. We add four fermion interactions and show that in the presence of these corrections the main interesting features of the model are still present and that the intrinsic attractive interaction can not be switched off. This study suggests to find GB corrections to equation of state of holographic QCD matter.
... Some bridges may presumably be drawn between our model and the AdS/QCD framework, although it is out of the scope of the present paper. The interested reader may find a detailed discussions of mesons in AdS/QCD in the review [47]. ...
We first quantize an action proposed by Casalbuoni and Gomis in 2014 that describes two massless relativistic scalar particles interacting via a conformally invariant potential. The spectrum is a continuum of massive states that may be interpreted as unparticles. We then obtain in a similar way the mass operator for a deformed action in which two terms are introduced that break the conformal symmetry: a mass term and an extra position-dependent coupling constant. A simple Ansatz for the latter leads to a mass operator with linear confinement in terms of an effective string tension σ. The quantized model is confining when σ≠0 and its mass spectrum shows Regge trajectories. We propose a tensionless limit in which highly excited confined states reduce to (gapped) unparticles. Moreover, the low-lying confined bound states become massless in the latter limit as a sign of conformal symmetry restoration and the ratio between their masses and σ stays constant. The originality of our approach is that it applies to both confining and conformal phases via an effective interacting model.
... One obtains a precise dictionary between field theory correlators and correlators of fields living inside the AdS spacetime [1][2][3][107][108][109] 2 . Holography is being used to study hydrodynamic transport coefficients, phase transitions in condensed matter systems, some aspects of QCD, open quantum systems, quantum chaos, black hole information paradox etc [13,40,[110][111][112][113][114][115][116][117][118] 3 . ...
In this review, we present the ongoing developments in bridging the gap between holography and experiments. To this end, we discuss information scrambling and models of quantum teleportation via Gao-Jafferis-Wall wormhole teleportation. We review the essential basics and summarize some of the recent works that have so far been obtained in quantum simulators towards a goal of realizing analogous models of holography in a lab.
... Some bridges may presumably be drawn between our model and the AdS/QCD framework, although it is out of the scope of the present paper. The interested reader may find a detailed discussions of mesons in AdS/QCD in the review [47]. ...
We first quantize the action proposed by Casalbuoni and Gomis in [Phys. Rev. D \textbf{90}, 026001 (2014)], an action that describes two massless relativistic scalar particles interacting via a conformally invariant potential. The spectrum is a continuum of massive states that may be interpreted as unparticles. We then obtain in a similar way the mass operator for a deformed action in which two terms are introduced that break the conformal symmetry: a mass term and an extra position-dependent coupling constant. A simple Ansatz for the latter leads to a mass operator with linear confinement in terms of an effective string tension $\sigma\,$. The quantized model is confining when $\sigma\neq0$ and its mass spectrum shows Regge trajectories. We propose a tensionless limit in which highly excited confined states reduce to (gapped) unparticles. Moreover, the low-lying confined bound states become massless in the latter limit as a sign of conformal symmetry restoration and the ratio between their masses and $\sqrt\sigma$ stays constant. The originality of our approach is that it applies to both confining and conformal phases via an effective interacting model.
... AdS/CFT correspondence offers a new possibility to tackle the difficulty of strongly coupled gauge theories, for reviews see Refs. [36][37][38][39]. Many efforts from both top-down and bottum-up approaches have been paid on examining nonperturbative QCD properties [40], e.g., QCD equation of state, phase transitions, fluid properties of quark-gluon plasma, meson spectra [41][42][43][44][45][46][47][48][49][50][51][52], baryon spectra [53][54][55], as well as in the glueball sector [56][57][58][59][60][61][62][63][64][65][66][67][68]. ...
We study the spectra of two-gluon glueballs and three-gluon oddballs and corresponding equation of state in $5$-dimensional deformed holographic QCD models in the graviton-dilaton system, where the metric, the dilaton field and dilaton potential are self-consistently solved from each other through the Einstein field equations and the equation of motion of the dilaton field. We compare the models by inputting the dilaton field, inputting the deformed metric and inputting the dilaton potential, and find that with only 2 parameters, the $5$-dimensional holographic QCD model predictions on glueballs/oddballs spectra in general are in good agreement with lattice results except two oddballs $0^{+-}$ and $2^{+-}$. From the results of glueballs/oddballs spectra at zero temperature and the equation of state at finite temperature, we observe that the model with quadratic dilaton field can simultaneously describe glueballs/oddballs spectra as well as equation of state of pure gluon system, and the model with quadratic deformed metric can describe glueballs/oddballs spectra, but its corresponding equation of state behaves more like $N_{f}=2+1$ quark matter, which is consistent with dimension analysis at UV boundary.
A bstract
We construct a new family of Type IIB backgrounds that are dual to five dimensional conformal field theories compactified and deformed by VEVs of certain operators. This generates an RG flow into a smooth background dual to non-SUSY gapped field theories in four dimensions. We study various holographic observables: a monotonic quantity associated with the number of degrees of freedom, Wilson loops that interpolate between conformal and confining behaviour with the possibility of screening, Entanglement Entropy, etc. We also give a prescription to compute the Holographic Complexity in this type of backgrounds and calculate the spectrum of spin-two glueballs of the field theories.
A bstract
A (toy) model for cold and luke-warm strongly-coupled nuclear matter at finite baryon density, is used to study neutrino transport. The complete charged current two-point correlators are computed in the strongly-coupled medium and their impact on neutrino transport is analyzed. The full result is compared with various approximations for the current correlators and the distributions, including the degenerate approximation, the hydrodynamic approximation as well as the diffusive approximation and we comment on their successes. Further improvements are discussed.
For a nonlinear partial differential equation for (pseudo)scalars in the bulk of Euclidean AdS4, arising from a truncation of 11-dimensional supergravity over \({\text{AdS}}_{4} \times S^{7} /Z_{k}\), we use math tools and in particular Adomian Decomposition Method, with initial data from near the boundary behavior of a special or general solution, although we focus on normalizable modes and Dirichlet boundary condition, to get perturbative series solutions (of the equation valid in probe approximation) for three special modes of \(m^2=4, 0, -9/4\). Meantime, we remind that for the skew-whiffed M2-branes background, there are Higgs-like (pseudo)scalars that make the equation homogeneous and provide spontaneous symmetry breaking. Then, with the setups and solutions in the bulk, where all supersymmetries and parity are broken, we swap the three fundamental representations of SO(8) for gravitino, deform the ABJM-like three-dimensional boundary actions with various corresponding \({\text{SU}}(4) \times U(1)\)-singlet operators made of fermions, scalars and SU(N) gauge fields, find new SO(4)-invariant instantons, and finally adjust the bulk and boundary solutions and confirm state-operator AdS\(_4\)/CFT\(_3\) correspondence.
The AdS/CFT correspondence and its generalization to gauge/gravity dualities provide a very useful approach into solving strongly coupled systems. We put this at work for the strongly coupled sector of Composite Higgs models. We work out relations between masses of proposed states in Composite Higgs. As a cross check we compare these results to existing lattice calculations for which we find good agreement.
We study thermal transitions in a domain wall AdS/QCD model. The model is based on the D5/probe D7 system with a discontinuous mass profile which restricts chiral fermions to 3+1 dimensional domain walls. Fluctuations on the domain wall are dual to the quark mass and condensate and reveal the relation between domain wall separation and the quark mass. The massive quarks exhibit a second order thermal, meson melting transition. Witten’s multitrace prescription can be used to interpret these configurations as having a dynamical mass from a Nambu-Jona-Lasinio interaction—here the transition is first order. Confinement can be introduced into the gauge sector by compactifying one direction of the D5. Compactification induces chiral symmetry breaking and there is a first order thermal restoration transition. If a NJL interaction is also introduced then the confinement and chiral symmetry breaking scales can be separated.
We study solitons in the context of Sakai-Sugimoto-Witten holographic model of QCD. In the large 't Hooft coupling limit, flat space instantons give an approximate description of baryons. We provide an ansatz through deforming the BPST instanton by zero modes and obtain a subleading correction to the effective action. We also consider the quantum mechanical description of the collective coordinates. The correction term appears as a perturbation to the potential of the Hamiltonian and hence we can derive a first order correction to the mass spectrum of baryons.
In this review article, we describe the role of holography in deciphering the physics of dense QCD matter, relevant for the description of compact stars and their binary mergers. We review the strengths and limitations of the holographic duality in describing strongly interacting matter at large baryon density, walk the reader through the most important results derived using the holographic approach so far, and highlight a number of outstanding open problems in the field. Finally, we discuss how we foresee holography contributing to compact-star physics in the coming years.
In this review, we present the ongoing developments in bridging the gap between holography and experiments. To this end, we discuss information scrambling and models of quantum teleportation via Gao–Jafferis–Wall wormhole teleportation. We review the essential basics and summarize some of the recent works that have so far been obtained in quantum simulators towards a goal of realizing analogous models of holography in a lab.
The complete absence of isolated quarks reaching particle detectors after high energy collisions suggests that some physical mechanism generates resistance to their propagation in the vacuum. In order to reveal such a mechanism, we analyze the fate of an infinitely heavy quark that is initially propagating in the vacuum with inertial motion. The non-perturbative structure of the vacuum is treated here using the gauge/ gravity correspondence, the isolated quark on the boundary gauge theory is dual to a trailing string moving in the bulk of a higher dimensional curved space. We find that, for a large class of non-conformal gauge theories with a holographic dual, the geometrical structure of the bulk geometry induces a drag force on the quark that moves in the vacuum. In addition, we show that for these gauge theories there will be the presence of such a drag force due to its vacuum whenever the dual bulk geometry generates a linear potential for a qq¯ pair. The relation of the linear qq¯ potential with the drag force on the isolated quark is a holographic piece of evidence that both phenomena are different manifestations of the confinement of quarks.
We establish a holographic QCD model for four flavors, where a light scalar field X and a heavy scalar field H are introduced separately. The H field is responsible for the breaking of SU(Nf=4) to SU(Nf=3). The ground state and its radial Regge excitation of meson spectra in the light flavor sector and heavy flavor sector as well as the light-heavy mesons are well in agreement with the Particle Data Group. Due to the additional introduction of the H field in the model, different Regge slopes for light and heavy mesons can be achieved.
The "periodic table" of strongly coupled gauge theories remains only sketchily understood. Holography has developed to the point where bottom up constructions can describe the spectrum of individual gauge theories (based on assumptions of their running) including quarks in different representations and higher dimension operators. I highlight the method with a "perfected" version of an AdS dual of QCD and results for composite higgs models with two representations of quarks. The method raises questions about the degree to which energy scales can be split in generic gauge theories including whether confinement and chiral symmetry breaking are linked.
We construct a new holographic description of QCD using domain wall fermions. The construction consists of probe D7 branes in a D5 brane geometry describing quarks on a (4+1)-dimensional defect in a (5+1)-dimensional gauge theory. We then compactify one dimension of the D5 to introduce confinement in the gauge degrees of freedom. In addition we allow a spatial dependent mass term for the D7 brane quarks to isolate chiral fermions on (3+1)-dimensional domain walls. The D7 world volume fields, when restricted to the domain wall position, provide an AdS/QCD description. We compute the spectrum and compare to data. We include higher dimension operators to systematically improve the description.
The mixing of graviphotons and dark brane photons to the Standard Model hypercharge is analyzed in full generality, in weakly-coupled string theory. Both the direct mixing as well as effective terms that provide mixing after inclusion of SM corrections are estimated to lowest order. The results are compared with Effective Field Theory (EFT) couplings, originating in a hidden large-N theory coupled to the SM where the dark photons are composite. The string theory mixing terms are typically subleading compared with the generic EFT couplings. The case where the hidden theory is a holographic theory is also analyzed, providing also suppressed mixing terms to the SM hypercharge.
We study all three-point functions of normalized chiral operators in D = 4, N = 4, U(N) supersymmetric Yang-Mills theory in the large N limit. We compute them for small 't Hooft coupling λ = g2Y MN ≪ 1 using free field theory and at strong coupling λ = g2Y MN ≫ 1 using the AdS/CFT correspondence. Surprisingly, we find the same answers in the two limits. We conjecture that at least for large N the exact answers are independent of λ.
We revisit the singular IIB supergravity solution describing
M-fractional 3-branes on the conifold [hep-th/0002159]. Its
5-form flux decreases, which we explain by showing that the relevant
Script N = 1 SUSY SU(N+M) × SU(N) gauge theory undergoes repeated
Seiberg-duality transformations in which N→N-M. Far in the IR
the gauge theory confines; its chiral symmetry breaking removes the
singularity of [hep-th/0002159] by
deforming the conifold. We propose a non-singular pure-supergravity
background dual to the field theory on all scales, with small curvature
everywhere if the `t Hooft coupling gsM is large. In the UV
it approaches that of [hep-th/0002159],
incorporating the logarithmic flow of couplings. In the IR the
deformation of the conifold gives a geometrical realization of chiral
symmetry breaking and confinement. We suggest that pure Script N = 1
Yang-Mills may be dual to strings propagating at small gsM on
a warped deformed conifold. We note also that the standard model itself
may lie at the base of a duality cascade.
We study the ∆I = 1/2 rule for kaon decays and the BK parameter for K 0 − ¯ K 0 mixing in a dual 5-dimensional holographic QCD model. We perform, in the chiral limit, computations of the relevant four-point current-current correlators, which depend upon self-interactions among the 5D bulk fields. Spontaneous chiral symmetry breaking (χSB) is realized through boundary conditions on the bulk fields. Numerical results are analyzed in comparison with QCD, chiral perturbation theory (χPT) and data, finding reasonable agreement with the experimental values of the g8 and g27 parameters describing the ∆I = 1/2, 3/2 decay channels.
We study the gauge/gravity dual of a finite temperature field theory at finite isospin chemical potential by considering a probe of two coincident D7-branes embedded in the AdS-Schwarzschild black hole background. The isospin chemical potential is obtained by giving a vacuum expectation value to the time component of the non-Abelian gauge field on the brane. The fluctuations of the non-Abelian gauge field on the brane are dual to the SU(2) flavor current in the field theory. For the embedding corresponding to vanishing quark mass, we calculate all Green functions corresponding to the components of the flavor current correlator. We discuss the physical properties of these Green functions, which go beyond linear response theory. In particular, we show that the isospin chemical potential leads to a frequency-dependent isospin diffusion coefficient.
We use the AdS/CFT correspondence to determine the rate of energy loss of a heavy quark moving through 𝒩 = 4 SU(Nc) supersymmetric Yang-Mills plasma at large 't Hooft coupling. Using the dual description of the quark as a classical string ending on a D7-brane, we use a complementary combination of analytic and numerical techniques to determine the friction coefficient as a function of quark mass. Provided strongly coupled 𝒩 = 4 Yang-Mills plasma is a good model for hot, strongly coupled QCD, our results may be relevant for charm and bottom physics at RHIC.
The addition of fundamental degrees of freedom to a theory which is dual (at low energies) to Script N = 2 SYM in 1+3 dimensions is studied. The gauge theory lives on a stack of Nc D5 branes wrapping an S2 with the appropriate twist, while the fundamental hypermultiplets are introduced by adding a different set of Nf D5-branes. In a simple case, a system of first order equations taking into account the backreaction of the Nf ~ Nc flavor branes is derived. From it, the modification of the holomorphic coupling is computed explicitly. Mesonic excitations are also discussed.
We consider field theories arising from a large number of D3-branes near singularities in F-theory. We study the theories at various conformal points, and compute, using their conjectured string theory duals, their large N spectrum of chiral primary operators. This includes, as expected, operators of fractional conformal dimensions for the theory at Argyres-Douglas points. Additional operators, which are charged under the (sometimes exceptional) global symmetries of these theories, come from the 7-branes. In the case of a D4 singularity we compare our results with field theory and find agreement for large N. Finally, we consider deformations away from the conformal points, which involve finding new supergravity solutions for the geometry produced by the 3-branes in the 7-brane background. We also discuss 3-branes in a general background.
We consider extra dimensional gauge theories on an interval. We first review the derivation of the consistent boundary conditions (BC's) from the action principle. These BC's include choices that give rise to the breaking of the gauge symmetries. The boundary conditions could be chosen to coincide with those commonly applied in orbifold theories, but there are many more possibilities. To investigate the nature of gauge symmetry breaking via BC's we calculate the elastic scattering amplitudes for longitudinal gauge bosons. We find that using a consistent set of BC's the terms in these amplitudes that explicitly grow with energy always cancel without having to introduce any additional scalar degree of freedom, but rather by the exchange of Kaluza-Klein (KK) gauge bosons. This suggests that perhaps the standard model Higgs boson could be completely eliminated in favor of some KK towers of gauge fields. We show that from the low-energy effective theory perspective this seems to be indeed possible. We display an extra dimensional toy model, where BC's introduce a symmetry breaking pattern and mass spectrum that resembles that in the standard model.
We find the gravity dual of a marginal deformation of Script N = 4 super Yang Mills, and discuss some of its properties. This deformation is intimately connected with an SL(2,Bbb R) symmetry of the gravity theory. The SL(2,Bbb R) transformation enables us to find the solutions in a simple way. These field theory deformations, sometimes called beta deformations, can be viewed as arising from a star product. Our method works for any theory that has a gravity dual with a U(1) × U(1) global symmetry which is realized geometrically. These include the field theories that live on D3 branes at the conifold or other toric singularities, as well as their cascading versions.
To endow the 𝒩 = 1⋆ SYM theory with quarks, we embed D7-brane probes into its gravity dual, known as the Polchinski-Strassler background. The non-vanishing 3-form flux G3 in the background is dual to mass terms for the three adjoint chiral superfields, deforming the 𝒩 = 4 SYM theory to the 𝒩 = 1⋆ SYM theory. We keep its three mass parameters independent. This generalizes our analysis in hep-th/0610276 for the 𝒩 = 2⋆ SYM theory. We work at second order in the mass perturbation, i.e. G3 and its backreaction on the background are considered perturbatively up to this order. We find analytic solutions for the embeddings which in general depend also on angular variables. We discuss the properties of the solutions and give error estimates on our approximation. By applying the method of holographic renormalization, we show that in all cases the embeddings are at least consistent with supersymmetry.
We construct backreacted D3/D7 supergravity backgrounds which are dual to four-dimensional 𝒩 = 1 and 𝒩 = 2 supersymmetric Yang-Mills at large Nc with flavor quarks in the fundamental representation of SU(Nc). We take into account the backreaction of D7-branes on either AdS5 × S5 or AdS5 × T1,1, or more generically on backgrounds where the space transverse to the D3-branes is Kähler. The construction of the backreacted geometry splits into two stages. First we determine the modification of the six-dimensional space transverse to the D3 due to the D7, and then we compute the warp factor due to the D3. The 𝒩 = 2 background corresponds to placing a single stack of Nf D7-branes in AdS5 × S5. Here the Kähler potential is known exactly, while the warp factor is obtained in certain limits as a perturbative expansion. By placing another D7′ probe in the backreacted D3/D7 background, we derive the effect of the D7-branes on the spectrum of the scalar fluctuations to first order in Nf. The two systems with 𝒩 = 1 supersymmetry that we discuss are D3/D7/D7' and D3/D7 on the conifold. In both cases, the Kähler potential is obtained perturbatively in the number of D7-branes. We provide all the ingredients necessary for the computation of each term in the expansion, and in each case give the first few terms explicitly. Finally, we comment on some aspects of the dual gauge theories.
We consider a noncritical five-dimensional string setup which could provide a dual description of QCD in the limit of large number of colors and flavors. The model corresponds to Nc color D3-branes and Nf D4/anti-D4-brane pairs supporting flavor degrees of freedom. The matching of the string model spectrum with the dual field theory one is considered. We discuss the consequences of the possible matching of the gravity modes with the light glueballs and the interpretation of the brane spectrum in Yang–Mills and QCD.
Two points on the Coulomb branch of 𝒩 = 4 super Yang Mills are investigated using their supergravity duals. By switching on condensates for the scalars in the 𝒩 = 4 multiplet with a form which preserves a subgroup of the original R-symmetry, disk and sphere configurations of D3-branes are formed in the dual supergravity background. The analytic, canonical metric for these geometries is formulated and the singularity structure is studied. Quarks are introduced into the corresponding field theories using D7-brane probes and the meson spectrum is calculated. For one of the condensate configurations, a mass gap is found and shown analytically to be present in the massless limit. It is also found that there is a stepped spectrum with eigenstate degeneracy in the limit of small quark masses and this result is shown analytically. In the second, similar deformation it is necessary to understand the full D3-D7 brane interaction to study the limit of small quark masses. For quark masses larger than the condensate scale the spectrum is calculated and shown to be discrete as expected.
We study supersymmetric embeddings of D-brane probes of different
dimensionality in the AdS5× La,b,c background of type
IIB string theory. In the case of D3-branes, we recover the
known three-cycles dual to the dibaryonic operators of the gauge theory
and we also find a new family of supersymmetric embeddings.
Supersymmetric configurations of D5-branes, representing fractional
branes, and of spacetime filling D7-branes (which can be used to add
flavor) are also found. Stable non supersymmetric configurations
corresponding to fat strings and domain walls are found as well.
Adding matter of mass m, in the fundamental representation of SU(N), to N=4 supersymmetric Yang-Mills theory, we study ``generalized quarkonium'' containing a (s)quark, an anti(s)quark, and J massless (or very light) adjoint particles. At large 't Hooft coupling $\lambda$ >> 1, the states of spin <= 1 are surprisingly light (Kruczenski et al., hep-th/0304032) and small (hep-th/0312071) with a J-independent size of order $\sqrt{\lambda}/m$. This ``trapping'' of adjoint matter in a region small compared with its Compton wavelength and compared to any confinement scale in the theory is an unfamiliar phenomenon, as it does not occur at small $\lambda$. We explore adjoint trapping further by considering the limit of large J. In particular, for J >> $\sqrt{\lambda}$ >> 1, we expect the trapping phenomenon to become unstable. Using Wilson loop methods, we show that a sharp transition, in which the generalized quarkonium states become unbound (for massless adjoints) occurs at $J \simeq 0.22 \sqrt{\lambda}$. If the adjoint scalars of N=4 are massive and the theory is confining (as, for instance, in N=1* theories) then the transition becomes a cross-over, across which the size of the states changes rapidly from ~$\sqrt{\lambda}/m$ to something of order the confinement scale ~ $\Lambda^{-1}$. Comment: Clarified transition with a better figure and improved presentation; added careful discussion of the small regime of validity of the Born-Oppenheimer computation and adjusted some remarks appropriately; also added two references
We address, in the AdS/CFT context, the issue of the universality of the couplings of the rho meson to other hadrons. Exploring some models, we find that generically the rho-dominance prediction f_\rho g_{\rho H H}=m_\rho^2 does not hold, and that g_{\rho H H} is not independent of the hadron H. However, we prove that, in any model within the AdS/QCD context, there are two limiting regimes where the g_{\rho H H}, along with the couplings of all excited vector mesons as well, become H-independent: (1) when H is created by an operator of large dimension, and (2) when H is a highly-excited hadron. We also find a sector of a particular model where universality for the rho coupling is exact. Still, in none of these cases need it be true that f_\rho g_\rho=m_\rho^2, although we find empirically that the relation does hold approximately (up to a factor of order two) within the models we have studied. Comment: 28 pages, 3 figures. ver 2: Comments about the commutability of two universal limits in the D3/D7 case corrected. Typos corrected. ver 3: Substantive revisions of certain calculations, with improved conventions, correction of typos, clarifications, new formulas, new figures; no changes in essential results or conclusions
Adding fundamental matter of mass m_Q to N=4 Yang Mills theory, we study quarkonium, and "generalized quarkonium" containing light adjoint particles. At large 't Hooft coupling the states of spin<=1 are anomalously light (Kruczenski et al., hep-th/0304032). We examine their form factors, and show these hadrons are unlike any known in QCD. By a traditional yardstick they appear infinite in size (as with strings in flat space) but we show that this is a failure of the yardstick. All of the hadrons are actually of finite size ~ \sqrt{g^2N}/m_Q, regardless of their radial excitation level and of how many valence adjoint particles they contain. Certain form factors for spin-1 quarkonia vanish in the large-g^2N limit; thus these hadrons resemble neither the observed J/Psi quarkonium states nor rho mesons. Comment: 57 pages, LaTeX, 5 figures
The nonperturbative properties of gauge theories in AdS4 are studied in dual supergravity by including light flavor quarks, which are introduced by a D7-brane embedding. Contrary to the Minkowski and dS4, the dilaton does not play any important dynamical role in the AdS4 case, and the characteristic properties like quark confinement and chiral symmetry breaking are realized mainly due to the geometry AdS4. The possible hadron spectra are also examined, and we find that the meson spectra are well described by the formula given by the field theory in AdS4, but the characteristic mass scale is modified by the gauge interactions for excited states.
We study a defect conformal field theory describing D3-branes intersecting over two space-time dimensions. This theory admits an exact Lagrangian description which includes both two- and four-dimensional degrees of freedom, has (4,4) supersymmetry and is invariant under global conformal transformations. Both two- and four-dimensional contributions to the action are conveniently obtained in a two-dimensional (2,2) superspace. In a suitable limit, the theory has a dual description in terms of a probe D3-brane wrapping an AdS3×S1 slice of AdS5×S5. We consider the AdS/CFT dictionary for this setup. In particular we find classical probe fluctuations corresponding to the holomorphic curve wy=cα′. These fluctuations are dual to defect fields containing massless two-dimensional scalars which parametrize the classical Higgs branch, but do not correspond to states in the Hilbert space of the CFT. We also identify probe fluctuations which are dual to BPS superconformal primary operators and to their descendants. A nonrenormalization theorem is conjectured for the correlators of these operators, and verified to order g2.
In studying the dynamics of large Nc, SU(Nc) gauge theory at finite temperature with fundamental quark flavors in the quenched approximation, we observe a first order phase transition. A quark condensate forms at finite quark mass, and the value of the condensate varies smoothly with the quark mass for generic regions in parameter space. At a particular value of the quark mass, there is a finite discontinuity in the condensate’s vacuum expectation value, corresponding to a first order phase transition. We study the gauge theory via its string dual formulation using the AdS/CFT conjecture, the string dual being the near-horizon geometry of Nc D3-branes at finite temperature, AdS5-Schwarzschild×S5, probed by a D7-brane. The D7-brane has topology R4×S3×S1 and allowed solutions correspond to either the S3 or the S1 shrinking away in the interior of the geometry. The phase transition represents a jump between branches of solutions having these two distinct D-brane topologies. The transition also appears in the meson spectrum.
We construct supergravity plus branes solutions, which we argue to be related to 4d N=1 SQCD with a quartic superpotential. The geometries depend on the ratio Nf/Nc which can be kept of order one, present a good singularity at the origin, and are weakly curved elsewhere. We support our field theory interpretation by studying a variety of features like R-symmetry breaking, instantons, Seiberg duality, Wilson loops and pair creation, running of couplings, and domain walls. In a second part of this paper, we address a different problem: the analysis of the interesting physics of different members of a family of supergravity solutions dual to (unflavored) N=1 SYM plus some UV completion.
The correspondence between supergravity (and string theory) on AdS space and boundary conformal field theory relates the thermodynamics of N = 4 super Yang-Mills theory in four dimensions to the thermodynamics of Schwarzschild black holes inAnti-de Sitter space. In this description, quantum phenomena such as the spontaneous breaking of the center of the gauge group, magnetic confinement, and the mass gap are coded in classical geometry. The correspondence makes it manifest that the entropy of a very large AdS Schwarzschild black hole must scale "holographically" with the volume of its horizon. By similar methods, one can also make a speculative proposal for the description of large N gauge theories in four dimensions without supersymmetry. © 2014 by World Scientific Publishing Co. Pte. Ltd. All rights reserved.
Numerical simulation of lattice-regulated QCD has become an important source of information about strong interactions. In the last few years there has been an explosion of techniques for performing ever more accurate studies on the properties of strongly interacting particles. Lattice predictions directly impact many areas of particle and nuclear physics theory and phenomenology. This book provides a thorough introduction to the specialized techniques needed to carry out numerical simulations of QCD: A description of lattice discretizations of fermions and gauge fields, methods for actually doing a simulation, descriptions of common strategies to connect simulation results to predictions of physical quantities, and a discussion of uncertainties in lattice simulations. More importantly, while lattice QCD is a well-defined field in its own right, it has many connections to continuum field theory and elementary particle physics phenomenology, which are carefully elucidated in this book. © 2006 by World Scientific Publishing Co. Pte. Ltd. All rights reserved.
We review the holographic correspondence between field theories and string/M theory, focusing on the relation between compactifications of string/M theory on Anti-de Sitter spaces and conformal field theories. We review the background for this correspondence and discuss its motivations and the evidence for its correctness. We describe the main results that have been derived from the correspondence in the regime that the field theory is approximated by classical or semiclassical gravity. We focus on the case of the N=4 supersymmetric gauge theory in four dimensions, but we discuss also field theories in other dimensions, conformal and non-conformal, with or without supersymmetry, and in particular the relation to QCD. We also discuss some implications for black hole physics.
String Theory comprises two volumes which give a comprehensive and pedagogic account of the subject. Volume 1, first published in 1998, provides a thorough introduction to the bosonic string. The first four chapters introduce the central ideas of string theory, the tools of conformal field theory and of the Polyakov path integral, and the covariant quantization of the string. The next three chapters treat string interactions: the general formalism, and detailed treatments of the tree level and one loop amplitudes. Chapter eight covers toroidal compactification and many important aspects of string physics, such as T-duality and D-branes. Chapter nine treats higher-order amplitudes, including an analysis of their finiteness and unitarity, and various nonperturbative ideas. An appendix giving a short course on path integral methods is included. This is an essential text and reference for graduate students and researchers interested in modern superstring theory.
In these lecture notes we first assemble the basic ingredients of supersymmetric gauge theories (particularly N=4 super-Yang-Mills theory), supergravity, and superstring theory. Brane solutions are surveyed. The geometry and symmetries of anti-de Sitter space are discussed. The AdS/CFT correspondence of Maldacena and its application to correlation functions in the the conformal phase of N=4 SYM are explained in considerable detail. A pedagogical treatment of holographic RG flows is given including a review of the conformal anomaly in four-dimensional quantum field theory and its calculation from five-dimensional gravity. Problem sets and exercises await the reader.
Recent results on QCD thermodynamics are presented. The nature of the
T>0 transition is determined, which turns out to be an analytic
cross-over. The absolute scale for this transition is calculated. The
temperature dependent static potential is given. The results were
obtained by using a Symanzik improved gauge and stout-link improved
fermionic action. In order to approach the continuum limit four
different sets of lattice spacings were used with temporal extensions
N_t=4, 6, 8 and 10 (they correspond to lattice spacings a \sim 0.3, 0.2,
0.15 and 0.12 fm). A new technique is presented, which --in contrast to
earlier methods-- enables one to determine the equation of state at very
large temperatures.
An accessible introduction to string theory, this book provides a
detailed and self-contained demonstration of the main concepts involved.
The first part deals with basic ideas, reviewing special relativity and
electromagnetism while introducing the concept of extra dimensions.
D-branes and the classical dynamics of relativistic strings are
discussed next, and the quantization of open and closed bosonic strings
in the light-cone gauge, along with a brief introduction to
superstrings. The second part begins with a detailed study of D-branes
followed by string thermodynamics. It discusses possible physical
applications, and covers T-duality of open and closed strings,
electromagnetic fields on D-branes, Born/Infeld electrodynamics,
covariant string quantization and string interactions. Primarily aimed
as a textbook for advanced undergraduate and beginning graduate courses,
it will also be ideal for a wide range of scientists and mathematicians
who are curious about string theory.
We find an exact, N=1 supersymmetric kink solution of 5d gauged
supergravity. We associate this solution with the RG flow from N=4 super
Yang-Mills theory, deformed by a relevant operator, to pure N=1 super
Yang-Mills in the IR. We test this identification by computing various
QFT quantities using the supergravity dual: the tension of electric and
magnetic strings and the gaugino condensate. As demanded by our
identification, our kink solution is a true deformation of N=4, that
exhibits confinement of quarks, magnetic screening, and spontaneous
chiral symmetry breaking.
Many examples of gravitational duals exist of theories that are highly
supersymmetric and conformal in the UV yet have the same massless states
as N=2,1,0 QCD. We discuss such theories with an explicit UV cutoff and
propose that, by tuning higher dimension operators at the cutoff by
hand, the effects of the extra matter states in the UV may be removed
from the IR physics. We explicitly work in the AdS Schwarzschild
description of QCD4 and tune the operator TrF by
relaxing the near horizon limit to reproduce the lattice 0
glueball mass results. We find that to reproduce the lattice data, the
IR and UV cutoffs lie close to each other and there is essentially no
AdS-like period between them. The improved geometry gives a better match
to the lattice data for 0 glueball masses.
We study N f D6-brane probes in the supergravity background dual to N c D4-branes compactified on a circle with supersymmetry-breaking boundary conditions. In the limit in which the resulting Kaluza-Klein modes decouple, the gauge theory reduces to non-supersymmetric, four-dimensional QCD with N c colours and N f << N c flavours. As expected, this decoupling is not fully realised within the supergravity/Born-Infeld approximation. For N f = 1 and massless quarks, m q = 0, we exhibit spontaneous chiral symmetry breaking by a quark condensate, ψ≠0, and find the associated massless `pion' in the spectrum. The latter becomes massive for m q > 0, obeying the Gell-Mann-Oakes-Renner relation: M π2 = −m qψ/fπ2 . In the case N f>1 we provide a holographic version of the Vafa-Witten theorem, which states that the U(N f) flavour symmetry cannot be spontaneously broken. Further, we find N f2−1 unexpectedly light pseudo-scalar mesons in the spectrum. We argue that these are not (pseudo-)Goldstone bosons and speculate on the string mechanism responsible for their lightness. We then study the theory at finite temperature and exhibit a phase transition associated with a discontinuity in ψ(T). D6/ pairs are also briefly discussed.
This book provides a concrete introduction to quantum fields on a lattice: a precise and non-perturbative definition of quantum field theory obtained by replacing continuous space-time by a discrete set of points on a lattice. The path integral on the lattice is explained in concrete examples using weak and strong coupling expansions. Fundamental concepts such as 'triviality' of Higgs fields and confinement of quarks and gluons into hadrons are described and illustrated with the results of numerical simulations. The book also provides an introduction to chiral symmetry and chiral gauge theory, as well as quantized non-abelian gauge fields, scaling and universality. Based on the lecture notes of a course given by the author, this book contains many explanatory examples and exercises, and is suitable as a textbook for advanced undergraduate and graduate courses.
Conformal techniques are applied to the calculation of integrals on AdSd+1 space which define correlators of composite operators in the superconformal field theory on the d-dimensional boundary. The 3-point amplitudes for scalar fields of arbitrary mass and gauge fields in the AdS supergravity are calculated explicitly. For three gauge fields we compare in detail with the known conformal structure of the SU(4) flavor current correlator 〈JiaJjbJkc〉 of the N = 4, d = 4 SU(N) SYM theory. Results agree with the free field approximation as would be expected from superconformal non-renormalization theorems. In studying the Ward identity relating 〈JiaOIOJ〉 to 〈OIOJ〉 for (non-marginal) scalar composite operators OI, we find that there is a subtlety in obtaining the normalization of 〈OIOJ〉 from the supergravity action integral.
It is shown that a wide class of non-Abelian gauge theories have, up to calculable logarithmic corrections, free-field-theory asymptotic behavior. It is suggested that Bjorken scaling may be obtained from strong-interaction dynamics based on non-Abelian gauge symmetry.
The gravitational quasi-normal frequencies of both stationary and
rotating black holes are calculated by constructing exact eigensolutions
to the radiative boundary-value problem of Chandrasekhar and Detweiler
(1975, 1976). The method is that employed by Jaffe (1934) in his
determination of the electronic spectra of the hydrogen molecule ion,
and analytic representations of the quasi-normal mode wavefunctions are
presented here for the first time. Numerical solution of Jaffe's
characteristic equation indicates that for each l-pole there is an
infinite number of damped Schwarzschild quasi-normal modes. The real
parts of the corresponding frequencies are bounded, but the imaginary
parts are not. Figures are presented that illustrate the trajectories
the five least-damped of these frequencies trace in the complex
frequency plane as the angular momentum of the black hole increases from
zero to near the Kerr limit of maximum angular momentum per unit mass, a
= M, where there is a coalescence of the more highly damped frequencies
to the purely real value of the critical frequency for superradiant
scattering.
We show that in parity-conserving vectorlike theories such as QCD, parity conservation is not spontaneously broken.
In this paper, two important transport observables in the relativistic heavy ion collider (RHIC) experiment---damping rate and jet quenching parameter---are calculated from an AdS/QCD model. A quark moving in the viscous medium such as the quark-gluon-plasma is modeled by an open string whose end point travels on the boundary of a deformed AdS5 black hole. The correction introduced via the deformed AdS5 is believed to help us better understand the data which is expected to be measured in the RHIC.
We argue that the existence of fundamental scalar fields constitutes a serious flaw of the Weinberg-Salam theory. A possible scheme without such fields is described. The symmetry breaking is induced by a new strongly interacting sector whose natural scale is of the order of a few TeV.
We study the family of ten-dimensional type-IIB supergravity solutions corresponding to renormalisation group flows from 𝒩 = 4 to 𝒩 = 2 supersymmetric SU(N) Yang-Mills theory. Part of the solution set corresponds to a submanifold of the Coulomb branch of the gauge theory, and we use a D3-brane probe to uncover details of this physics. At generic places where supergravity is singular, the smooth physics of the probe yields the correct one-loop form of the effective low energy gauge coupling. The probe becomes tensionless on a ring at finite radius. Supergravity flows which end on this ``enhançon'' ring correspond to the vacua where extra massless degrees of freedom appear in the gauge theory, and the gauge coupling diverges there. We identify an SL(2,ℤ) duality action on the enhançon ring which relates the special vacua, and comment on the massless dyons within them. We propose that the supergravity solution inside the enhançon ring should be excised, since the probe's tension is unphysical there.
In these lecture notes we first assemble the basic ingredients of supersymmetric gauge theories (particularly N=4 super-Yang-Mills theory), supergravity, and superstring theory. Brane solutions are surveyed. The geometry and symmetries of anti-de Sitter space are discussed. The AdS/CFT correspondence of Maldacena and its application to correlation functions in the the conformal phase of N=4 SYM are explained in considerable detail. A pedagogical treatment of holographic RG flows is given including a review of the conformal anomaly in four-dimensional quantum field theory and its calculation from five-dimensional gravity. Problem sets and exercises await the reader.
We study nonsupersymmetric fermion mass and condensate deformations of the AdS conformal field theory correspondence. The five dimensional supergravity flows are lifted to a complete and remarkably simple ten dimensional background. A brane probe analysis shows that when all the fermions have an equal mass a positive mass is generated for all six scalar fields leaving nonsupersymmetric Yang-Mills theory in the deep infrared. We numerically determine the potential, produced by the background, in the Schrödinger equation relevant to the study of O++ glueballs. The potential is a bounded well, providing evidence of stability and for a discrete, confined spectrum. The geometry can also describe the supergravity background around an (unstable) fuzzy 5-brane.
It is shown that the dynamical symmetry breakdown of a gauge symmetry can in some cases lead to simple relations among the masses of intermediate vector bosons.
We study the ΔI=1/2 rule for kaon decays and the BK parameter for K0-K̅ 0 mixing in a dual 5-dimensional holographic QCD model. We perform, in the chiral limit, computations of the relevant four-point current-current correlators, which depend upon self-interactions among the 5D bulk fields. Spontaneous chiral symmetry breaking (χSB) is realized through boundary conditions on the bulk fields. Numerical results are analyzed in comparison with QCD, chiral perturbation theory (χPT) and data, finding reasonable agreement with the experimental values of the g8 and g27 parameters describing the ΔI=1/2, 3/2 decay channels.