Miguel Salvado Costa

Escola Superior de Hotelaria e Turismo do Estoril

A bstract We propose and explore the Regge limit for correlation functions of five local primary operators in conformal field theories. After reviewing some features of Regge theory for flat-space scattering amplitudes, we analyze the analytic structure of conformal blocks both in position and Mellin space in the Regge limit and propose an extensio...

We propose and explore the Regge limit for correlation functions of five local primary operators in conformal field theories. After reviewing some features of Regge theory for flat-space scattering amplitudes, we analyse the analytic structure of conformal blocks both in position and Mellin space in the Regge limit and propose an extension of confo...

A bstract Higher-point functions of scalar operators are a rich observable in CFTs, as they contain OPE data involving multiple spinning operators. We derive the lightcone blocks for five- and six-point functions in the snowflake channel and use them to bootstrap these correlators in the lightcone limit. As a result we determine the large spin expa...

A bstract The boundary correlation functions for a Quantum Field Theory (QFT) in an Anti-de Sitter (AdS) background can stay conformally covariant even if the bulk theory undergoes a renormalization group (RG) flow. Studying such correlation functions with the numerical conformal bootstrap leads to non-perturbative constraints that must hold along...

Higher-point functions of scalar operators are a rich observable in CFTs, as they contain OPE data involving multiple spinning operators. We derive the lightcone blocks for five- and six-point functions in the snowflake channel and use them to bootstrap these correlators in the lightcone limit. As a result we determine the large spin expansion of O...

The boundary correlation functions for a Quantum Field Theory (QFT) in an Anti-de Sitter (AdS) background can stay conformally covariant even if the bulk theory undergoes a renormalization group (RG) flow. Studying such correlation functions with the numerical conformal bootstrap leads to non-perturbative constraints that must hold along the entire...

A bstract We derive an optical theorem for perturbative CFTs which computes the double discontinuity of conformal correlators from the single discontinuities of lower order correlators, in analogy with the optical theorem for flat space scattering amplitudes. The theorem takes a purely multiplicative form in the CFT impact parameter representation...

We derive an optical theorem for perturbative CFTs which computes the double discontinuity of conformal correlators from the single discontinuities of lower order correlators, in analogy with the optical theorem for flat space scattering amplitudes. The theorem takes a purely multiplicative form in the CFT impact parameter representation used to de...

A bstract We construct a new class of differential operators that naturally act on AdS harmonic functions. These are weight shifting operators that change the spin and dimension of AdS representations. Together with CFT weight shifting operators, the new operators obey crossing equations that relate distinct representations of the conformal group....

We construct a new class of differential operators that naturally act on AdS harmonic functions. These are weight shifting operators that change the spin and dimension of AdS representations. Together with CFT weight shifting operators, the new operators obey crossing equations that relate distinct representations of the conformal group. We apply o...

We consider the effect of including a non-minimal coupling between a $U(1)$ vector gauge field and the graviton Regge trajectory in holographic QCD models. This coupling describes the QCD interaction between the quark bilinear electromagnetic current and the Pomeron. We test this new coupling against DIS data at low Bjorken $x$ and obtain an excell...

We consider the Regge limit of the CFT correlation functions $\langle {\cal J} {\cal J} {\cal O}{\cal O}\rangle$ and $\langle TT {\cal O}{\cal O}\rangle$, where ${\cal J}$ is a vector current, $T$ is the stress tensor and ${\cal O}$ is some scalar operator. These correlation functions are related by a type of Fourier transform to the AdS phase shif...

We consider the Regge limit of the CFT correlation functions $\langle {\cal J} {\cal J} {\cal O}{\cal O}\rangle$ and $\langle TT {\cal O}{\cal O}\rangle$, where ${\cal J}$ is a vector current, $T$ is the stress tensor and ${\cal O}$ is some scalar operator. These correlation functions are related by a type of Fourier transform to the AdS phase shif...

We develop a formalism where the hard and soft pomeron contributions to high energy scattering arise as leading Regge poles of a single kernel in holographic QCD. The kernel is obtained using effective field theory inspired by Regge theory of a 5-d string theory. It describes the exchange of higher spin fields in the graviton Regge trajectory that...

We develop a formalism where the hard and soft pomeron contributions to high energy scattering arise as leading Regge poles of a single kernel in holographic QCD. The kernel is obtained using effective field theory inspired by Regge theory of a 5-d string theory. It describes the exchange of higher spin fields in the graviton Regge trajectory that...

We numerically construct asymptotically $AdS_4$ solutions to Einstein-Maxwell-dilaton theory. These have a dipolar electrostatic potential turned on at the conformal boundary $S^2\times \mathbb{R}_t$. We find two classes of geometries: $AdS$ soliton solutions that encode the full backreaction of the electric field on the $AdS$ geometry without a ho...

We numerically construct asymptotically $AdS_4$ solutions to Einstein-Maxwell-dilaton theory. These have a dipolar electrostatic potential turned on at the conformal boundary $S^2\times \mathbb{R}_t$. We find two classes of geometries: $AdS$ soliton solutions that encode the full backreaction of the electric field on the $AdS$ geometry without a ho...

We consider solutions in Einstein–Maxwell theory with a negative cosmological constant that asymptote to global AdS 4 with conformal boundary . At the sphere at infinity we turn on a space-dependent electrostatic potential, which does not destroy the asymptotic AdS behaviour. For simplicity we focus on the case of a dipolar electrostatic potential....

This paper develops a method to compute any bosonic conformal block as a series expansion in the optimal radial coordinate introduced by Hogervorst and Rychkov. The method reduces to the known result when the external operators are all the same scalar operator, but it allows to compute conformal blocks for external operators with spin. Moreover, we...

In this paper we derive the projectors to all irreducible SO(d) representations (traceless mixed-symmetry tensors) that appear in the partial wave decomposition of a conformal correlator of four stress-tensors in d dimensions. These projectors are given in a closed form for arbitrary length $l_1$ of the first row of the Young diagram. The appearanc...

This paper develops a method to compute any bosonic conformal block as a series expansion in the optimal radial coordinate introduced by Hogervorst and Rychkov. The method reduces to the known result when the external operators are all the same scalar operator, but it allows to compute conformal blocks for external operators with spin. Moreover, we...

In this paper we derive the projectors to all irreducible SO(d) representations (traceless mixed-symmetry tensors) that appear in the partial wave decomposition of a conformal correlator of four stress-tensors in d dimensions. These projectors are given in a closed form for arbitrary length $l_1$ of the first row of the Young diagram. The appearanc...

We study the graviton Regge trajectory in Holographic QCD as a model for high energy scattering processes dominated by soft pomeron exchange. This is done by considering spin J fields from the closed string sector that are dual to glueball states of even spin and parity. In particular, we construct a model that governs the analytic continuation of...

From the perspective of AdS/CFT the Pomeron is identified with a Reggeized Graviton, while the Odderons correspond to Reggeized anti-symmetric AdS5 Kalb-Ramond tensor-fields. In this paper, we consider the strong coupling expansion of the dimension of the leading twist operators dual to these Regge trajectories, Δ(j), to determine its analytic cont...

We generalize the embedding formalism for conformal field theories to the case of general operators with mixed symmetry. The index-free notation encoding symmetric tensors as polynomials in an auxiliary polarization vector is extended to mixed-symmetry tensors by introducing a new commuting or anticommuting polarization vector for each row or colum...

We construct the black hole geometry dual to the deconfined phase of the BMN matrix model at strong 't Hooft coupling. We approach this solution from the limit of large temperature where it is approximately that of the non-extremal D0-brane geometry with a spherical $S^8$ horizon. This geometry preserves the $SO(9)$ symmetry of the matrix model tri...

From the perspective of AdS/CFT the Pomeron is identified with a Reggeized Graviton, while the Odderons correspond to Reggeized anti-symmetric $AdS_5$ Kalb-Ramond tensor-fields. In this paper, we consider the strong coupling expansion of the dimension of the leading twist operators dual to these Regge trajectories, $\Delta(j)$, to determine its ana...

We develop the embedding formalism to describe symmetric traceless tensors in Anti-de Sitter space. We use this formalism to construct the bulk-to-bulk propagator of massive spin J fields and check that it has the expected short distance and massless limits. We also and a split representation for the bulk-to-bulk propagator, by writing it as an int...

We study two kinematical limits, the Regge limit and the Lorentzian OPE limit, of the four-point function of the stress-tensor multiplet in Super Yang-Mills at weak coupling. We explain how both kinematical limits are controlled by the leading twist operators. We use the known expression of the four-point function up to three loops, to extract the...

We use gauge/gravity duality to study vector meson (J/{\Psi}, {\rho}_0, {\Omega}, {\Phi}) production in electron-proton scattering, in the limit of high center of mass energy at fixed momentum transfer, corresponding to the limit of low Bjorken x, where the process is dominated by pomeron exchange. Our approach considers the pomeron at strong coupl...

In the past decade overwhelming evidence has emerged for a conjectured duality between a wide class of gauge theories in d dimensions and string theories on asymptotically AdS_{d+1} spaces. We apply this duality to scattering processes that occur via Pomeron exchange. First we develop the Pomeron in string theory, as done by Brower, Polchinski, Str...

We generalize Regge theory to correlation functions in conformal field theories. This is done by exploring the analogy between Mellin amplitudes in AdS/CFT and S-matrix elements. In the process, we develop the conformal partial wave expansion in Mellin space, elucidating the analytic structure of the partial amplitudes. We apply the new formalism t...

We use gauge/gravity duality to study deeply virtual Compton scattering (DVCS) in the limit of high center of mass energy at fixed momentum transfer, corresponding to the limit of low Bjorken x, where the process is dominated by the exchange of the pomeron. Using conformal Regge theory we review the form of the amplitude for pomeron exchange, both...

For conformal field theories in arbitrary dimensions, we introduce a method to derive the conformal blocks corresponding to the exchange of a traceless symmetric tensor appearing in four point functions of operators with spin. Using the embedding space formalism, we show that one can express all such conformal blocks in terms of simple differential...

We develop the embedding formalism for conformal field theories, aimed at doing computations with symmetric traceless operators of arbitrary spin. We use an index-free notation where tensors are encoded by polynomials in auxiliary polarization vectors. The efficiency of the formalism is demonstrated by computing the tensor structures allowed in n-p...

Using the approximate conformal invariance of QCD at high energies we consider a simple AdS black disk model to describe saturation in DIS. Deep inside saturation the structure functions have the same power law scaling, F(T) similar to F(L) similar to x(-omega), where. is related to the expansion rate of the black disk with energy. Furthermore, the...

Using the approximate conformal invariance of QCD at high energies we consider a simple anti-de Sitter black disk model to describe saturation in deep inelastic scattering. Deep inside saturation the structure functions have the same power law scaling, F{T}∼F{L}∼x{-ω}, where ω is related to the expansion rate of the black disk with energy. Furtherm...

We study the effect of marginal and irrelevant deformations on the renormalization of operators near a CFT fixed point. New divergences in a given operator are determined by its OPE with the operator D that generates the deformation. This provides a scheme to compute the couplings a_DAB between the operator D and two arbitrary operators O_A and O_B...

We analysed two special cases of the double-Kerr solution describing a system of two stationary co-axial Kerr black holes, with equal mass and either the same or opposite angular momentum. These cases are asymptotically flat and obey the axis condition, but there is always a strut (i.e. a conical singularity) between the black holes, preventing the...

We consider the Regge limit of a CFT correlation function of two vector and two scalar operators, as appropriate to study small-x deep inelastic scattering in \( \mathcal{N} = 4 \) SYM or in QCD assuming approximate conformal symmetry. After clarifying the nature of the Regge limit for a CFT correlator, we use its conformal partial wave expansion t...

We consider the asymptotically flat double-Kerr solution for two equal mass black holes with either the same or opposite angular momentum and with a massless strut between them. For fixed angular momentum and mass, the angular velocity of two co-rotating Kerr black holes decreases as they approach one another, from the Kerr value at infinite separa...

Using the inverse scattering method we construct a six-parameter family of exact, stationary, asymptotically flat solutions of the 4+1 dimensional vacuum Einstein equations, with U(1)2 rotational symmetry. It describes the superposition of two Myers-Perry black holes, each with a single angular momentum parameter, both in the same plane. The black...

We analyze deep inelastic scattering at small Bjorken x, using the approximate conformal invariance of QCD at high energies. Hard Pomeron exchanges are resummed eikonally, restoring unitarity at large values of the phase shift in the dual anti-de Sitter (AdS) geometry. At weak coupling this phase is imaginary, corresponding to a black disk in AdS s...

Using the inverse scattering method we construct a six-parameter family of exact, stationary, asymptotically flat solutions of the 4+1 dimensional vacuum Einstein equations, with U(1) 2 ro-tational symmetry. It describes the superposition of two Myers-Perry black holes, each with a single angular momentum parameter, both in the same plane. The blac...

Using the inverse scattering method we construct a six-parameter family of exact, stationary, asymptotically flat solutions of the 4+1 dimensional vacuum Einstein equations, with U(1)^2 rotational symmetry. It describes the superposition of two Myers-Perry black holes, each with a single angular momentum parameter, both in the same plane. The black...

We consider correlators of N=4 super Yang Mills of the form A ~ < O_1 O_2 O*_1 O*_2 >, where the operators O_1 and O_2 are scalar primaries. In particular, we analyze this correlator in the planar limit and in a Lorentzian regime corresponding to high energy interactions in AdS. The planar amplitude is dominated by a Regge pole whose nature varies...

We derive an eikonal approximation to high energy interactions in Anti-de Sitter spacetime, by generalizing a position space derivation of the eikonal amplitude in flat space. We are able to resum, in terms of a generalized phase shift, ladder and cross ladder graphs associated to the exchange of a spin j field, to all orders in the coupling consta...

We introduce the impact-parameter representation for conformal field theory correlators of the form A ~ < O_1 O_2 O_1 O_2 >. This representation is appropriate in the eikonal kinematical regime, and approximates the conformal partial-wave decomposition in the limit of large spin and dimension of the exchanged primary. Using recent results on the tw...

We initiate a program to generalize the standard eikonal approximation to compute amplitudes in Anti-de Sitter spacetimes. Inspired by the shock wave derivation of the eikonal amplitude in flat space, we study the two-point function ~ 11shock in the presence of a shock wave in Anti-de Sitter, where 1 is a scalar primary operator in the dual conform...

We give evidence in favour of a string/black hole transition in the case of BPS fundamental string states of the Heterotic string. Our analysis goes beyond the counting of degrees of freedom and considers the evolution of dynamical quantities in the process. As the coupling increases, the string states decrease their size up to the string scale wh...

We conjecture chronology is protected in string theory due to the condensation of light winding strings near closed null curves. This condensation triggers a Hagedorn phase transition, whose end-point target space geometry should be chronological. Contrary to conventional arguments, chronology is protected by an infrared effect. We support this con...

It is well known that spherical D-branes are nucleated in the presence of an external RR electric field. Using the description of D-branes as solitons of the tachyon field on non-BPS D-branes, we show that the brane nucleation process can be seen as the decay of the tachyon false vacuum. This process can describe the decay of flux-branes in string...

We conjecture that, in certain cases, quantum dynamics is consistent in the presence of closed timelike curves. We consider time dependent orbifolds of three dimensional Minkowski space describing, in the limit of large AdS radius, BTZ black holes inside the horizon. Although perturbative unitarity fails, we show that, for discrete values of the gr...

It is well known that spherical D-branes are nucleated in the presence of an external RR electric field. Using the description of D-branes as solitons of the tachyon field on non-BPS D-branes, we show that the brane nucleation process can be seen as the decay of the tachyon false vacuum. This process can describe the decay of flux-branes in string...

We analyze the classical stability of string cosmologies driven by the dynamics of orientifold planes. These models are related to time-dependent orbifolds, and resolve the orbifold singularities which are otherwise problematic by introducing orientifold planes. In particular, we show that the instability discussed by Horowitz and Polchinski for pu...

We study the physics of D-branes in the presence of constant Ramond-Ramond potentials. In the string field theory context, we first develop a general formalism to analyze open strings in gauge trivial closed string backgrounds, and then apply it both to the RNS string and within Berkovits' covariant formalism, where the results have the most natura...

We consider new cosmological solutions with a collapsing, an intermediate and an expanding phase. The boundary between the expanding (collapsing) phase and the intermediate phase is seen by comoving observers as a cosmological past (future) horizon. The solutions are naturally embedded in string and M-theory. In the particular case of a two-dimensi...

We consider the generalization to String and M-theory of the Melvin solution. These are flux p-branes which have (p+1)-dimensional Poincare invariance and are associated to an electric (p+1)-form field strength along their worldvolume. When a stack of Dp-branes is placed along the worldvolume of a flux (p+3)-brane it will expand to a spherical D(p+...

We consider accelerated D-branes in the linear approximation to the supergravity limit of string theory. Such branes emit scalar, gauge field and gravitational radiation. A Larmor-type formula for the emitted scalar radiation is obtained.

We study some aspects of the Kaluza-Klein Melvin solution in M-theory. The associated magnetic field has a maximal critical value $B=\pm 1/R$ where $R$ is the radius of the compactification circle. It is argued that the Melvin background of type IIA with magnetic field $B$ and of type 0A with magnetic field $B'=B-1/R$ are equivalent. Evidence for t...

We revisit the geometry representing l collinear Schwarzschild black holes. It is seen that the black holes' horizons are deformed by their mutual gravitational attraction. The geometry has a string like conical singularity that connects the holes but has nevertheless a well defined action. Using standard gravitational thermodynamics techniques we...

We consider the SU(N) Super Yang Mills theory on the Coulomb branch with gauge symmetry broken to S(U(N1)×U(N2)). By integrating the W particles, the effective action near the IR SU(Ni) conformal fixed points is seen to be a deformation of the Super Yang Mills theory by a non-renormalized, irrelevant, dimension 8 operator. The correction to the two...

We calculate the classical cross-section for absorption of a minimally coupled scalar in the double-centered D3-brane geometry. The dual field theory has gauge symmetry broken to S(U(N1) × U(N2)) and is on the Coulomb branch of 𝒩 = 4 Super Yang-Mills theory. Our analysis is valid at energy scales much smaller than the W particles mass, giving logar...

The radiation emitted by accelerated fundamental strings and D-branes is studied within the linear approximation to the supergravity limit of string theory. We show that scalar, gauge field and gravitational radiation is generically emitted by such branes. In the case where an external scalar field accelerates the branes, we derive a Larmor-type fo...

The radiation emitted by accelerated fundamental strings and D-branes is studied within the linear approximation to the supergravity limit of string theory. We show that scalar, gauge field and gravitational radiation is generically emitted by such branes. In the case where an external scalar field accelerates the branes, we derive a Larmor-type fo...

We study intersecting D-branes in type 0 string theories and show that the D$p_{\pm}$-brane bound states obey similar intersecting rules as the D$p$-branes of the type II theories. The D$5_{\pm}$-D$1_{\pm}$ brane system is studied in detail. We show that the corresponding near-horizon geometry is the $AdS_3\times S^3\times T^4$ space and that there...

D-branes have played a crucial role in understanding many aspects of string theory ([1] and references there in). At the heart of Polchinski’s proposal is the fact that the excitations of these solitons have a well defined quantum mechanical description: D-branes are extended objects with the property that open strings can end on them. The D-brane...

A D-5-brane bound state with a self-dual field strength on a 4-torus is considered. In a particular case this model reproduces the D5-D1 brane bound state usually used in the string theory description of 5-dimensional black holes. In the limit where the brane dynamics decouples from the bulk the Higgs and Coulomb branches of the theory on the brane...

We consider a supersymmetric system of D-5-branes compactified on T4 × S1 with a self-dual background field strength on T4 and carrying left-moving momentum along S1. The corresponding supergravity solution describes a five-dimensional black hole with a regular horizon. The entropy of this black hole may be explained in terms of the Landau degenera...

We consider the supergravity solution describing a configuration of intersecting D4-branes with non-vanishing world-volume gauge fields. The entropy of such a black hole is calculated in terms of the D-branes quantised charges. The non-extreme solution is also considered and the corresponding thermodynamical quantities are calculated in terms of a...

We start with Bogomol'nyi-Prasad-Sommerfield- (BPS) saturated configurations of two (orthogonally) intersecting M-branes and use the electromagnetic duality or dimensional reduction along a boost, in order to obtain new p-brane bound states. In the first case the resulting configurations are interpreted as BPS-saturated nonthreshold bound states of...

We generalise all the known supersymmetric composite M-branes to the corresponding black configurations. Thermodynamical formulae is written by using the simple rules to construct these black branes. Comment: 14 pages, latex. Revised version to appear in Nuclear Physics B

We present a class of Kałuża-Klein electrically charged black p-brane solutions of 10-dimensional, type 11A superstring theory. Uplifting to 11 dimensions these solutions are studied in the context of M-theory. They can be interpreted either as a p + 1 extended object trapped around the 11th dimension along which momentum is flowing or as a boost o...

We present new supersymmetric solutions of D = 11 supergravity obtained by intersecting the brane configuration interpreted as a 2-brane lying within a 5-brane. Some of these solutions can be boosted along a common string and/or superposed with a Kaluza-Klein monopole, We also present a new embedding of the extreme four-dimensional dyonic black hol...