[Show abstract][Hide abstract] ABSTRACT: In recent papers, it was hypothesized that there exist dissipationless quantum liquids, i.e., liquids with zero or vanishingly small viscosity and zero entropy production, which nevertheless have nontrivial second-order transport coefficients. A natural candidate for a dissipationless liquid is the hypothetical conformal quantum liquid, whose holographically dual description in the infrared limit is given by the five-dimensional Gauss-Bonnet gravity. It is known that shear viscosity in that theory can be made arbitrarily small as the Gauss-Bonnet coupling parameter approaches a critical value. We evaluate the transport coefficients of a Gauss-Bonnet liquid (nonperturbatively in the coupling parameter; three of the six coefficients were previously unknown) and consider the zero-viscosity limit. We show that three of the five second-order coefficients are nonzero in this limit, but they do not satisfy the criterion of zero entropy production. Hence, the holographic Gauss-Bonnet liquid is not a dissipationless quantum liquid.
[Show abstract][Hide abstract] ABSTRACT: We compute the 't Hooft coupling correction to the infinite coupling
expression for the second order transport coefficient $\lambda_2$ in ${\cal
N}=4$ $SU(N_c)$ supersymmetric Yang-Mills theory at finite temperature in the
limit of infinite $N_c$, which originates from the $R^4$ terms in the low
energy effective action of the dual type IIB string theory. Using this result,
we show that the identity involving the three second order transport
coefficients, $2 \eta \tau_\Pi - 4 \lambda_1 - \lambda_2 =0$, previously shown
by Haack and Yarom to hold universally in relativistic conformal field theories
with string dual descriptions to leading order in supergravity approximation,
holds also at next to leading order in this theory. We also compute corrections
to transport coefficients in a (hypothetical) strongly interacting conformal
fluid arising from the generic curvature squared terms in the corresponding
dual gravity action (in particular, Gauss-Bonnet action), and show that the
identity holds to linear order in the higher-derivative couplings. We discuss
potential implications of these results for the near-equilibrium entropy
production rate at strong coupling.
Journal of High Energy Physics 12/2014; 2015(3). DOI:10.1007/JHEP03(2015)007 · 6.11 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: We use gauge-gravity duality to study the temperature dependence of the zero
sound mode and the fundamental matter diffusion mode in the strongly coupled
{\cal N}=4 SU(N_c) supersymmetric Yang-Mills theory with N_f {\cal N}=2
hypermultiplets in the N_c>>1, N_c>>N_f limit, which is holographically
realized via the D3/D7 brane system. In the high density limit \mu>>T, three
regimes can be identified in the behavior of these modes, analogous to the
collisionless quantum, collisionless thermal and hydrodynamic regimes of a
Landau Fermi-liquid. The transitions between the three regimes are
characterized by the parameters T/\mu and (T/\mu)^2 respectively, and in each
of these regimes the modes have a distinctively different temperature and
momentum dependence. The collisionless-hydrodynamic transition occurs when the
zero sound poles of the density-density correlator in the complex frequency
plane collide on the imaginary axis to produce a hydrodynamic diffusion pole.
We observe that the properties characteristic of a Landau Fermi-liquid zero
sound mode are present in the D3/D7 system despite the atypical T^6/\mu^3
temperature scaling of the specific heat and an apparent lack of a directly
identifiable Fermi surface.
[Show abstract][Hide abstract] ABSTRACT: Quasinormal modes are eigenmodes of dissipative systems. Perturbations of classical gravitational backgrounds involving black holes or branes naturally lead to quasinormal modes. The analysis and classification of the quasinormal spectra require solving non-Hermitian eigenvalue problems for the associated linear differential equations. Within the recently developed gauge-gravity duality, these modes serve as an important tool for determining the near-equilibrium properties of strongly coupled quantum field theories, in particular their transport coefficients, such as viscosity, conductivity and diffusion constants. In astrophysics, the detection of quasinormal modes in gravitational wave experiments would allow precise measurements of the mass and spin of black holes as well as new tests of general relativity. This review is meant as an introduction to the subject, with a focus on the recent developments in the field.
[Show abstract][Hide abstract] ABSTRACT: Quantum liquids are characterized by the distinctive properties such as the low-temperature behavior of heat capacity and the spectrum of low-energy quasiparticle excitations. In particular, at low temperature, Fermi liquids exhibit the zero sound, predicted by Landau in 1957 and subsequently observed in liquid He-3. In this Letter, we ask whether such characteristic behavior is present in theories with a holographically dual description. We consider a class of gauge theories with fundamental matter fields whose holographic dual in the appropriate limit is given in terms of the Dirac-Born-Infeld action in anti-de Sitter space. We find that these systems also exhibit a sound mode at zero temperature despite having a non-Fermi-liquid behavior of the specific heat. These properties suggest that holography identifies a new type of quantum liquid which potentially could be experimentally realized in strongly correlated systems.
[Show abstract][Hide abstract] ABSTRACT: Quantum liquids are characterized by the distinctive properties such as the low temperature behavior of heat capacity and the spectrum of low-energy quasiparticle excitations. In particular, at low temperature, Fermi liquids exhibit the zero sound, predicted by L. D. Landau in 1957 and subsequently observed in liquid He-3. In this paper, we ask a question whether such a characteristic behavior is present in theories with holographically dual description. We consider a class of gauge theories with fundamental matter fields whose holographic dual in the appropriate limit is given in terms of the Dirac-Born-Infeld action in AdS_{p+1} space. An example of such a system is the N=4 SU(N_c) supersymmetric Yang-Mills theory with N_f massless N=2 hypermultiplets at strong coupling, finite baryon number density, and low temperature. We find that these systems exhibit a zero sound mode despite having a non-Fermi liquid type behavior of the specific heat. These properties suggest that holography identifies a new type of quantum liquids.
[Show abstract][Hide abstract] ABSTRACT: The membrane paradigm approach to black hole physics introduces the notion of a stretched horizon as a fictitious time-like surface endowed with physical characteristics such as entropy, viscosity and electrical conductivity. We show that certain properties of the stretched horizons are encoded in the quasinormal spectrum of black holes. We compute analytically the lowest quasinormal frequency of a vector-type perturbation for a generic black hole with a translationally invariant horizon (black brane) in terms of the background metric components. The resulting dispersion relation is identical to the one obtained in the membrane paradigm treatment of the diffusion on stretched horizons. Combined with the Buchel–Liu universality theorem for the membrane's diffusion coefficient, our result means that in the long wavelength limit the black brane spectrum of gravitational perturbations exhibits a universal, purely imaginary quasinormal frequency. In the context of gauge–gravity duality, this provides yet another (third) proof of the universality of shear viscosity to entropy density ratio in theories with gravity duals.
Physics Letters B 07/2008; 670(4-5-670):442-445. DOI:10.1016/j.physletb.2008.11.028 · 6.13 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: We consider second-order viscous hydrodynamics in conformal field theories at finite temperature. We show that conformal invariance imposes powerful constraints on the form of the second-order corrections. By matching to the AdS/CFT calculations of correlators, and to recent results for Bjorken flow obtained by Heller and Janik, we find three (out of five) second-order transport coefficients in the strongly coupled = 4 supersymmetric Yang-Mills theory. We also discuss how these new coefficents can arise within the kinetic theory of weakly coupled conformal plasmas. We point out that the Müller-Israel-Stewart theory, often used in numerical simulations, does not contain all allowed second-order terms and, frequently, terms required by conformal invariance.
Journal of High Energy Physics 04/2008; 2008(04):100. DOI:10.1088/1126-6708/2008/04/100 · 6.11 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: The holographic dual of large-Nc super-Yang-Mills coupled to a small number of flavours of fundamental matter, Nf << Nc, is described by Nf probe D7-branes in the gravitational background of Nc black D3-branes. This system undergoes a first order phase transition characterised by the `melting' of the mesons. We study the high temperature phase in which the D7-branes extend through the black hole horizon. In this phase, we compute the spectral function for vector, scalar and pseudoscalar modes on the D7-brane probe. We also compute the diffusion constant for the flavour currents.
Journal of High Energy Physics 07/2007; 11(11). DOI:10.1088/1126-6708/2007/11/091 · 6.11 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: We review recent progress in applying the AdS/CFT correspondence to finite-temperature field theory. In particular, we show how the hydrodynamic behavior of field theory is reflected in the low-momentum limit of correlation functions computed through a real-time AdS/CFT prescription, which we formulate. We also show how the hydrodynamic modes in field theory correspond to the low-lying quasinormal modes of the AdS black p-brane metric. We provide a proof of the universality of the viscosity/entropy ratio within a class of theories with gravity duals and formulate a viscosity bound conjecture. Possible implications for real systems are mentioned.
Annual Review of Nuclear and Particle Science 05/2007; 57(1). DOI:10.1146/annurev.nucl.57.090506.123120 · 11.26 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: By weakly gauging one of the U(1) subgroups of the R-symmetry group, N=4 super-Yang-Mills theory can be coupled to electromagnetism, thus allowing a computation of photon production and related phenomena in a QCD-like non-Abelian plasma at both weak and strong coupling. We compute photon and dilepton emission rates from finite temperature N=4 supersymmetric Yang-Mills plasma both perturbatively at weak coupling to leading order, and non-perturbatively at strong coupling using the AdS/CFT duality conjecture. Comparison of the photo-emission spectra for N=4 plasma at weak coupling, N=4 plasma at strong coupling, and QCD at weak coupling reveals several systematic trends which we discuss. We also evaluate the electric conductivity of N=4 plasma in the strong coupling limit, and to leading-log order at weak coupling. Current-current spectral functions in the strongly coupled theory exhibit hydrodynamic peaks at small frequency, but otherwise show no structure which could be interpreted as well-defined thermal resonances in the high-temperature phase. Comment: 32 pages v2: added improved discussion of choice and normalization of EM current
Journal of High Energy Physics 07/2006; 2006(12). DOI:10.1088/1126-6708/2006/12/015 · 6.11 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: The transport properties of certain strongly coupled thermal gauge theories can be determined from their effective description
in terms of gravity or superstring theory duals. Here we provide a short summary of the results for the shear and bulk viscosity,
charge diffusion constant, and the speed of sound in supersymmetric strongly interacting plasmas. We also outline a general
algorithm for computing transport coefficients in any gravity dual. The algorithm relates the transport coefficients to the
coefficients in the quasinormal spectrum of five-dimensional black holes in asymptotically anti de Sitter space.
European Physical Journal A 06/2006; 29(1):77-81. DOI:10.1140/epja/i2005-10301-2 · 2.74 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: We use the gauge-gravity duality conjecture to compute spectral functions of the stress-energy tensor in finite-temperature N = 4 supersymmetric Yang-Mills theory in the limit of large N(c) and large 't Hooft coupling. The spectral functions exhibit peaks characteristic of hydrodynamic modes at small frequency, and oscillations at intermediate frequency. The nonperturbative spectral functions differ qualitatively from those obtained in perturbation theory. The results may prove useful for lattice studies of transport processes in thermal gauge theories.
[Show abstract][Hide abstract] ABSTRACT: We consider hydrodynamics of N=4 supersymmetric SU(N_c) Yang-Mills plasma at a nonzero density of R-charge. In the regime of large N_c and large 't Hooft coupling the gravity dual description involves an asymptotically Anti- de Sitter five-dimensional charged black hole solution of Behrnd, Cvetic and Sabra. We compute the shear viscosity as a function of chemical potentials conjugated to the three U(1) \subset SO(6)_R charges. The ratio of the shear viscosity to entropy density is independent of the chemical potentials and is equal to 1/4\pi. For a single charge black hole we also compute the thermal conductivity, and investigate the critical behavior of the transport coefficients near the boundary of thermodynamic stability. Comment: 21 pages, 1 figure; v2: typos fixed, references added; v3: typo in eq. 2.18 fixed
Journal of High Energy Physics 01/2006; 2006(03). DOI:10.1088/1126-6708/2006/03/052 · 6.11 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: Using gauge theory/gravity duality we study sound wave propagation in strongly coupled non-conformal gauge theory plasma. We compute the speed of sound and the bulk viscosity of N=2∗ supersymmetric SU(Nc) Yang–Mills plasma at a temperature much larger than the mass scale of the theory in the limit of large Nc and large 't Hooft coupling. The speed of sound is computed both from the equation of state and the hydrodynamic pole in the stress–energy tensor two-point correlation function. Both computations lead to the same result. Bulk viscosity is determined by computing the attenuation constant of the sound wave mode.
Nuclear Physics B 07/2005; 733(1-733):160-187. DOI:10.1016/j.nuclphysb.2005.11.005 · 3.93 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: Quasinormal frequencies of electromagnetic and gravitational perturbations in asymptotically AdS spacetime can be identified with poles of the corresponding real-time Green's functions in a holographically dual finite temperature field theory. The quasinormal modes are defined for gauge-invariant quantities which obey incoming-wave boundary condition at the horizon and Dirichlet condition at the boundary. As an application, we explicitly find poles of retarded correlation functions of R-symmetry currents and the energy-momentum tensor in strongly coupled finite temperature N=4 supersymmetric SU(Nc) Yang-Mills theory in the limit of large Nc. Comment: 28 pages; v2: typos fixed, ref. added
[Show abstract][Hide abstract] ABSTRACT: We study the hydrodynamics of the high-energy phase of Little String Theory. The poles of the retarded two-point function of the stress energy tensor contain information about the speed of sound and the kinetic coefficients, such as shear and bulk viscosity. We compute this two-point function in the dual string theory and analytically continue it to Lorentzian signature. We perform an independent check of our results by the Lorentzian supergravity calculation in the background of non-extremal NS5-branes. The speed of sound vanishes at the Hagedorn temperature. The ratio of shear viscosity to entropy density is equal to the universal value 1/4\pi and does not receive \alpha' corrections. The ratio of bulk viscosity to entropy density equals 1/10\pi. We also compute the R-charge diffusion constant. In addition to the hydrodynamic singularities, the correlators have an infinite series of finite-gap poles, and a massless pole with zero attenuation. Comment: 30 pages, 3 figures; harvmac
Journal of High Energy Physics 06/2005; 2005(10). DOI:10.1088/1126-6708/2005/10/027 · 6.11 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: The ratio of shear viscosity to volume density of entropy can be used to characterize how close a given fluid is to being perfect. Using string theory methods, we show that this ratio is equal to a universal value of variant Planck's over 2pi/4pik(B) for a large class of strongly interacting quantum field theories whose dual description involves black holes in anti-de Sitter space. We provide evidence that this value may serve as a lower bound for a wide class of systems, thus suggesting that black hole horizons are dual to the most ideal fluids.
[Show abstract][Hide abstract] ABSTRACT: Gauge theory–gravity duality predicts that the shear viscosity of N=4 supersymmetric SU(Nc) Yang–Mills plasma at temperature T in the limit of large Nc and large 't Hooft coupling is independent of the coupling and equals to . In this paper, we compute the leading correction to the shear viscosity in inverse powers of 't Hooft coupling using the α′-corrected low-energy effective action of type IIB string theory. We also find the correction to the ratio of shear viscosity to the volume entropy density (equal to 1/4π in the limit of infinite coupling). The correction to 1/4π scales as with a positive coefficient.
Nuclear Physics B 02/2005; 707(1-2-707):56-68. DOI:10.1016/j.nuclphysb.2004.11.055 · 3.93 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: We extend the correspondence between black hole physics and thermodynamics to non-equilibrium processes. The shear viscosity is shown to correspond to the absorption cross section of low-energy graviton by the black hole. We show that the ratio of shear viscosity to volume density of entropy in theories with gravity duals is equal to a universal value of h/(4pi). We conjecture that this value is a lower limit on the ratio of shear viscosity to entropy density for a very wide class of systems. Possible applications of this viscosity bound conjecture are mentioned.