Showing papers on "AdS/CFT correspondence published in 2007"
TL;DR: In this paper, a covariant generalization of the holographic entanglement entropy proposal of hep-th/0603001 is proposed to understand the time-dependence of entropy in generic quantum field theories.
Abstract: With an aim towards understanding the time-dependence of entanglement entropy in generic quantum field theories, we propose a covariant generalization of the holographic entanglement entropy proposal of hep-th/0603001. Apart from providing several examples of possible covariant generalizations, we study a particular construction based on light-sheets, motivated in similar spirit to the covariant entropy bound underlying the holographic principle. In particular, we argue that the entanglement entropy associated with a specified region on the boundary in the context of the AdS/CFT correspondence is given by the area of a co-dimension two bulk surface with vanishing expansions of null geodesics. We demonstrate our construction with several examples to illustrate its reduction to the holographic entanglement entropy proposal in static spacetimes. We further show how this proposal may be used to understand the time evolution of entanglement entropy in a time varying QFT state dual to a collapsing black hole background. Finally, we use our proposal to argue that the Euclidean wormhole geometries with multiple boundaries should be regarded as states in a non-interacting but entangled set of QFTs, one associated to each boundary.
2,047 citations
TL;DR: In this article, the authors 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 they formulate.
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 quasi-normal modes of the AdS black p-brane metric. We provide 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.
706 citations
TL;DR: In this paper, the amplitude of planar planar amplitudes in = 4 super Yang Mills at strong 't Hooft coupling is approximated by classical surfaces in AdS5 space, and a prescription for computing processes involving local operators and asymptotic states with a fixed number of gluons is given.
Abstract: In this article we consider n gluon color ordered, planar amplitudes in = 4 super Yang Mills at strong 't Hooft coupling. These amplitudes are approximated by classical surfaces in AdS5 space. We compute the value of the amplitude for a particular kinematic configuration for a large number of gluons and find that the result disagrees with a recent guess for the exact value of the amplitude. Our results are still compatible with a possible relation between amplitudes and Wilson loops. In addition, we also give a prescription for computing processes involving local operators and asymptotic states with a fixed number of gluons. As a byproduct, we also obtain a string theory prescription for computing the dual of the ordinary Wilson loop, TrPeiA, with no couplings to the scalars. We also evaluate the quark-antiquark potential at two loops.
490 citations
TL;DR: In this paper, the authors consider charge transport properties of 2+1 dimensional conformal field theories at non-zero temperature, and show that the effects of particle-vortex duality on the hydrodynamic-to-collisionless crossover function of SO(8) Rcurrents can be obtained in the large N limit by applying the AdS/CFT correspondence to Mtheory.
Abstract: We consider charge transport properties of 2+1 dimensional conformal field theories at non-zero temperature. For theories with only Abelian U(1) charges, we describe the action of particle-vortex duality on the hydrodynamic-to-collisionless crossover function: this leads to powerful functional constraints for self-dual theories. For N=8 supersymmetric, SU(N) Yang-Mills theory at the conformal fixed point, exact hydrodynamic-to-collisionless crossover functions of the SO(8) Rcurrents can be obtained in the large N limit by applying the AdS/CFT correspondence to Mtheory. In the gravity theory, fluctuating currents are mapped to fluctuating gauge fields in the background of a black hole in 3+1 dimensional anti-de Sitter space. The electromagnetic self-duality of the 3+1 dimensional theory implies that the correlators of the R-currents obey a functional constraint similar to that found from particle-vortex duality in 2+1 dimensional Abelian theories. Thus the 2+1 dimensional, superconformal Yang Mills theory obeys a “holographic self duality” in the large N limit, and perhaps more generally.
433 citations
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TL;DR: In this paper, the conductivity of massive = 2 hypermultiplet fields at finite baryon number density in an = 4 SU(Nc) super-Yang-Mills theory plasma in the large Nc, large 't Hooft coupling limit was derived.
Abstract: We use the AdS/CFT correspondence to compute the conductivity of massive = 2 hypermultiplet fields at finite baryon number density in an = 4 SU(Nc) super-Yang-Mills theory plasma in the large Nc, large 't Hooft coupling limit. The finite baryon density provides charge carriers analogous to electrons in a metal. An external electric field then induces a finite current which we determine directly. Our result for the conductivity is good for all values of the mass, external field and density, modulo statements about the yet-incomplete phase diagram. In the appropriate limits it agrees with known results obtained from analyzing small fluctuations around equilibrium. For large mass, where we expect a good quasi-particle description, we compute the drag force on the charge carriers and find that the answer is unchanged from the zero density case. Our method easily generalizes to a wide class of systems of probe branes in various backgrounds.
388 citations
TL;DR: In this article, the complete Type IIB supergravity solutions with 16 supersymmetries were obtained on the manifold AdS4? S 2? S2?S2?? with SO(2, 3)? SO(3)?SO(3)-symmetric symmetry in terms of two holomorphic functions on a Riemann surface.
Abstract: The complete Type IIB supergravity solutions with 16 supersymmetries are obtained on the manifold AdS4 ? S2 ? S2 ? ? with SO(2, 3) ? SO(3) ? SO(3) symmetry in terms of two holomorphic functions on a Riemann surface ?, which generally has a boundary. This is achieved by reducing the BPS equations using the above symmetry requirements, proving that all solutions of the BPS equations solve the full Type IIB supergravity field equations, mapping the BPS equations onto a new integrable system akin to the Liouville and Sine-Gordon theories, and mapping this integrable system to a linear equation which can be solved exactly. Amongst the infinite class of solutions, a non-singular Janus solution is identified which provides the AdS/CFT dual of the maximally supersymmetric Yang-Mills interface theory discovered recently. The construction of general classes of globally non-singular solutions, including fully back-reacted AdS5 ? S5 and supersymmetric Janus doped with D5 and/or NS5 branes, is deferred to a companion paper [1].
369 citations
TL;DR: In this paper, the Zamolodchikov-Faddeev algebra for the superstring sigma model on AdS5 ×S 5 was discussed and the canonical su(2|2) 2 invariant S-matrix satisfy- ing the standard Yang-Baxter and crossing symmetry equations.
Abstract: We discuss the Zamolodchikov-Faddeev algebra for the superstring sigma-model on AdS5 ×S 5 . We find the canonical su(2|2) 2 invariant S-matrix satisfy- ing the standard Yang-Baxter and crossing symmetry equations. Its near-plane-wave expansion matches exactly the leading order term recently obtained by the direct per- turbative computation. We also show that the S-matrix obtained by Beisert in the gauge theory framework does not satisfy the standard Yang-Baxter equation, and, as a consequence, the corresponding ZF algebra is twisted. The S-matrices in gauge and string theories however are physically equivalent and related by a non-local transformation of the basis states which is explicitly constructed.
331 citations
TL;DR: In this article, the expectation values of Wilson loops in strongly coupled plasma of N = 4 super Yang-Mills (SYM) theory were derived for the case of heavy ion collisions.
Abstract: Expectation values of Wilson loops define the nonperturbative properties of the hot medium produced in heavy ion collisions that arise in the analysis of both radiative parton energy loss and quarkonium suppression. We use the AdS/CFT correspondence to calculate the expectation values of such Wilson loops in the strongly coupled plasma of N = 4 super Yang-Mills (SYM) theory, allowing for the possibility that the plasma may be moving with some collective flow velocity as is the case in heavy ion collisions. We obtain the N = 4 SYM values of the jet quenching parameter ˆ q, which describes the energy loss of a hard parton in QCD, and of the velocity-dependence of the quark-antiquark screening length for a moving dipole as a function of the angle between its velocity and its orientation. We show that if the quark-gluon plasma is flowing with velocity vf at an angle θ with respect to the trajectory of a hard parton, the jet quenching parameteris modified by a factor γf (1 − vf cos θ), and show that this result applies in QCD as in N = 4 SYM. We discuss the relevance of the lessons we are learning from all these calculations to heavy ion collisions at RHIC and at the LHC. Furthermore, we discuss the relation between our results and those obtained in other theories with gravity duals, showing in particular that the ratio betweenin any two conformal theories with gravity duals is the square root of the ratio of their central charges. This leads us to conjecture that in nonconformal theories ˆ q defines a quantity that always decreases
330 citations
TL;DR: In this paper, an infinite class of regular solutions with varying dilaton, and non-zero 3-form fluxes were derived for AdS5 × S5 with 16 supersymmetries.
Abstract: Regularity and topology conditions are imposed on the exact Type IIB solutions on AdS4 × S2 × S2 × Σ with 16 supersymmetries, which were derived in a companion paper [1]. We construct an infinite class of regular solutions with varying dilaton, and non-zero 3-form fluxes. Our solutions may be viewed as the fully back-reacted geometries of AdS5 × S5 (or more generally, Janus) doped with D5 and/or NS5 branes. The solutions are parametrized by the choice of an arbitrary genus g hyper-elliptic Riemann surface Σ with boundary, all of whose branch points are restricted to lie on a line. For genus 0, the Janus solution with 16 supersymmetries and 6 real parameters is recovered; its topology coincides with that of AdS5 × S5. The genus g ≥ 1 solutions are parametrized by a total of 4g + 6 real numbers, 2g−1 of which are the real moduli of Σ. The solutions have 2g + 2 asymptotic AdS5 × S5 regions, g three-spheres with RR 3-form charge, and another g with NSNS 3-form charge. Collapse of consecutive branch points of Σ yields singularities which correspond to D5 and NS5 branes in the probe limit. It is argued that the AdS/CFT dual gauge theory to each of our solutions consists of a 2+1-dimensional planar interface on which terminate 2g + 2 half-Minkowski 3+1-dimensional space-time = 4 super-Yang-Mills theories. Generally, the = 4 theory in each Minkowski half-space-time may have an independent value of the gauge coupling, and the interface may support various operators, whose interface couplings are further free parameters of the dual gauge theory.
266 citations
TL;DR: In this article, the validity of the recently proposed dressed, asymptotic Bethe ansatz for the planar AdS/CFT system is indeed limited at weak coupling by operator wrapping effects.
Abstract: We prove that the validity of the recently proposed dressed, asymptotic Bethe ansatz for the planar AdS/CFT system is indeed limited at weak coupling by operator wrapping effects. This is done by comparing the Bethe ansatz predictions for the four-loop anomalous dimension of finite-spin twist-two operators to BFKL constraints from high-energy scattering amplitudes in gauge theory. We find disagreement, which means that the ansatz breaks down for length-two operators at four-loop order. Our method supplies precision tools for multiple all-loop tests of the veracity of any yet-to-be constructed set of exact spectral equations. Finally we present a conjecture for the exact four-loop anomalous dimension of the family of twist-two operators, which includes the Konishi field.
259 citations
TL;DR: In this article, a general and systematic treatment of multi-trace deformations in the AdS/CFT correspondence in the large N limit is presented, pointing out and clarifying subtleties relating to the formulation of the boundary value problem on a conformal boundary.
Abstract: We present a general and systematic treatment of multi-trace deformations in the AdS/CFT correspondence in the large N limit, pointing out and clarifying subtleties relating to the formulation of the boundary value problem on a conformal boundary. We then apply this method to study multi-trace deformations in the presence of a scalar VEV, which requires the coupling to gravity to be taken into account. We show that supergravity solutions subject to `mixed' boundary conditions are in one-to-one correspondence with critical points of the holographic effective action of the dual theory in the presence of a multi-trace deformation, and we find a number of new exact analytic solutions involving a minimally or conformally coupled scalar field satisfying `mixed' boundary conditions. These include the generalization to any dimension of the instanton solution recently found in hep-th/0611315. Finally, we provide a systematic method for computing the holographic effective action in the presence of a multi-trace deformation in a derivative expansion away from the conformal vacuum using Hamilton-Jacobi theory. Requiring that this effective action exists and is bounded from below reproduces recent results on the stability of the AdS vacuum in the presence of `mixed' boundary conditions.
TL;DR: In this article, an eikonal approximation to high energy interactions in anti-de Sitter spacetime was derived by generalizing a position space derivation of the amplitude in flat space.
Abstract: 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 constant Using the AdS/CFT correspondence, the resulting amplitude determines the behavior of the dual conformal field theory four-point function for small values of the cross ratios, in a Lorentzian regime Finally we show that the phase shift is dominated by graviton exchange and computes, in the dual CFT, the anomalous dimension of the double trace primary operators O-1 partial derivativepartial derivative O-2 of large dimension and spin, corresponding to the relative motion of the two interacting particles The results are valid at strong t'Hooft coupling and are exact in the 1/N expansion
TL;DR: In this paper, the authors introduced the impact parameter representation for conformal field theory correlators of the form A similar to (O 1O2O1O2), which approximates the conformal partial wave decomposition in the limit of large spin and dimension of the exchanged primary.
TL;DR: In this paper, the strong subadditivity property of the entanglement entropy in conformal field theories has been verified via direct calculations using annuli or cusps and the Bousso bound.
Abstract: Recently, a holographic computation of the entanglement entropy in conformal field theories has been proposed via the AdS/CFT correspondence. One of the most important properties of the entanglement entropy is known as the strong subadditivity. This requires that the entanglement entropy should be a concave function with respect to geometric parameters. It is a non-trivial check on the proposal to see if this property is indeed satisfied by the entropy computed holographically. In this paper we examine several examples which are defined by annuli or cusps, and confirm the strong subadditivity via direct calculations. Furthermore, we conjecture that Wilson loop correlators in strongly coupled gauge theories satisfy the same relation. We also discuss the relation between the holographic entanglement entropy and the Bousso bound.
TL;DR: In this paper, the authors derived the eikonal amplitude in the presence of a shock wave in Anti-de Sitter spacetimes, where O1 is a scalar primary operator in the dual conformal field theory.
Abstract: 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 E ∼ hO 1O1i shock in the presence of a shock wave in Anti-de Sitter, where O1 is a scalar primary operator in the dual conformal field theory. At tree level in the gravitational coupling, we relate the shock two-point function E to the discontinuity across a kinematical branch cut of the conformal field theory four-point function A ∼ hO 1O2O1O2i , where O2 creates the shock geometry in Anti-de Sitter. Finally, we extend the above results by computing E in the presence of shock waves along the horizon of Schwarzschild BTZ black holes. This work gives new tools for the study of Planckian physics in Anti-de Sitter spacetimes.
TL;DR: In this paper, the authors reformulated the bulk-to-boundary map in as local a way as possible, and showed that the support on the boundary can always be reduced to a compact region spacelike separated from the bulk point.
Abstract: To gain insight into how bulk locality emerges from the holographic conformal field theory (CFT), we reformulate the bulk-to-boundary map in as local a way as possible. In previous work, we carried out this program for Lorentzian anti-de Sitter (AdS), and showed the support on the boundary could always be reduced to a compact region spacelike separated from the bulk point. In the present work the idea is extended to a complexified boundary, where spatial coordinates are continued to imaginary values. This continuation enables us to represent a local bulk operator as a CFT operator with support on a finite disc on the complexified boundary. We treat general AdS in Poincar\'e coordinates and ${\mathrm{AdS}}_{3}$ in Rindler coordinates. We represent bulk operators inside the horizon of a Banados-Teitelboim-Zanelli (BTZ) black hole and we verify that the correct bulk two-point functions are reproduced, including the divergence when one point hits the BTZ singularity. We comment on the holographic description of black holes formed by collapse and discuss locality and holographic entropy counting at finite $N$.
TL;DR: In this article, the authors developed the spacetime aspects of the computation of partition functions for string/M-theory on AdS3 × M. This leads to a better understanding of the "Farey tail" expansion of Dijkgraaf et al. from the point of view of bulk physics.
Abstract: We develop the spacetime aspects of the computation of partition functions for string/M-theory on AdS3 × M. Subleading corrections to the semi-classical result are included systematically, laying the groundwork for comparison with CFT partition functions via the AdS3/CFT2 correspondence. This leads to a better understanding of the "Farey tail" expansion of Dijkgraaf et. al. from the point of view of bulk physics. Besides clarifying various issues, we also extend the analysis to the N = 2 setting with higher derivative effects included.
TL;DR: In this article, the authors investigate gauge/gravity duals with flavour for which pure-gauge Kalb-Ramond B fields are turned on in the background, into which a D7 brane probe is embedded.
Abstract: We investigate gauge/gravity duals with flavour for which pure-gauge Kalb-Ramond B fields are turned on in the background, into which a D7 brane probe is embedded. First we consider the case of a magnetic field in two of the spatial boundary directions. We show that at finite temperature, i.e. in the AdS-Schwarzschild background, the B field has a stabilizing effect on the mesons and chiral symmetry breaking occurs for a sufficiently large value of the B field. Then we turn to the electric case of a B field in the temporal direction and one spatial boundary direction. In this case, there is a singular region in which it is necessary to turn on a gauge field on the brane in order to ensure reality of the brane action. We find that the brane embeddings are attracted towards this region. Far away from this region, in the weak field case at zero temperature, we investigate the meson spectrum and find a mass shift similar to the Stark effect.
TL;DR: In this article, a 1-loop correction E 1 to the energy of folded string in A d S 5 × S 5 (carrying spin S and momentum J in S 5 ) using a long string approximation in which S ≫ J ≫ 1 according to the AdS/CFT the function E 1 should represent first subleading correction to strong coupling expansion of anomalous dimension of higher twist SL ( 2 ) sector operators of the form Tr D S Z J ǫ.
TL;DR: In this paper, the effect of double-trace deformation on the partition function and conformal anomaly of a CFTd at large N and its dual picture in AdSd+1 was studied.
Abstract: We study the effect of a relevant double-trace deformation on the partition function (and conformal anomaly) of a CFTd at large N and its dual picture in AdSd+1 Three complementary previous results are brought into full agreement with each other: bulk [1] and boundary [2] computations, as well as their formal identity [3] We show the exact equality between the dimensionally regularized partition functions or, equivalently, fluctuation determinants involved A series of results then follows: (i) equality between the renormalized partition functions for all d; (ii) for all even d, correction to the conformal anomaly; (iii) for even d, the mapping entails a mixing of UV and IR effects on the same side (bulk) of the duality, with no precedent in the leading order computations; and finally, (iv) a subtle relation between overall coefficients, volume renormalization and IR-UV connection All in all, we get a clean test of the AdS/CFT correspondence beyond the classical SUGRA approximation in the bulk and at subleading O(1) order in the large-N expansion on the boundary
TL;DR: In this paper, an expanding boost-invariant plasma at strong coupling using the AdS/CFT correspondence for super Yang-Mills theory was considered and the relaxation time in second order viscous hydrodynamics was found to be around 30 times shorter than weak coupling expectations.
Abstract: We consider an expanding boost-invariant plasma at strong coupling using the AdS/CFT correspondence for $\mathcal{N}=4$ super Yang-Mills theory. We determine the relaxation time in second order viscous hydrodynamics and find that it is around 30 times shorter than weak coupling expectations. We find that the nonsingularity of the dual geometry in the string frame necessitates turning on the dilaton which leads to a nonvanishing expectation value for $\mathrm{tr}{F}^{2}$ behaving like ${\ensuremath{\tau}}^{\ensuremath{-}10/3}$.
TL;DR: In this paper, the authors consider the supergravity backgrounds that correspond to supersymmetric Wilson line operators in the context of AdS/CFT correspondence and obtain necessary conditions for a supergravity background that preserves the same symmetry as the supersymmetrical Wilson lines.
Abstract: We consider the supergravity backgrounds that correspond to supersymmetric Wilson line operators in the context of AdS/CFT correspondence. We study the gravitino and dilatino conditions of the IIB supergravity under the appropriate ansatz, and obtain some necessary conditions for a supergravity background that preserves the same symmetry as the supersymmetric Wilson lines. The supergravity solutions are characterized by continuous version of Maya diagrams. This diagram is related to the eigenvalue distribution of the Gaussian matrix model. We also consider the similar backgrounds of the 11-dimensional supergravity.
TL;DR: In this article, the behavior of correlators of Polyakov loops and other operators in = 4 supersymmetric Yang-Mills theory at non-zero temperature was examined using the AdS/CFT correspondence, and the implications for Debye screening in this strongly coupled non-Abelian plasma, and comparisons with available results for thermal QCD, were discussed.
Abstract: Using the AdS/CFT correspondence, we examine the behavior of correlators of Polyakov loops and other operators in = 4 supersymmetric Yang-Mills theory at non-zero temperature. The implications for Debye screening in this strongly coupled non-Abelian plasma, and comparisons with available results for thermal QCD, are discussed.
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TL;DR: In this article, a generalized Regge theory for conformal field theory 4-point functions of the form A ~ O(x_1) O(2(x-2), O(1(x)-3), O((x-4) O((1, x)-2, x-3)), where the operators O(i) are scalar primaries.
Abstract: We analyze conformal field theory 4-point functions of the form A ~ O_1(x_1) O_2(x_2) O_1(x_3) O_2(x_4), where the operators O_i are scalar primaries. We show that, in the Lorentzian regime, the limit x_1 -> x_3 is dominated by the exchange of conformal partial waves of highest spin. When partial waves of arbitrary spin contribute to A, the behavior of the Lorentzian amplitude for x_1 -> x_3 must be analyzed using complex-spin techniques, leading to a generalized Regge theory for CFT's. Whenever the CFT is dual to a string theory, the string tree-level contribution A_tree to the amplitude A presents a Regge pole corresponding the a gravi-reggeon exchange. In this case, we apply the impact parameter representation for CFT amplitudes, previously developed, to analyze multiple reggeon exchanges in the eikonal limit. As an example, we apply these general techniques to N=4 super-Yang-Mills theory in d=4 in the limit of large 't Hooft coupling, including the leading string corrections to pure graviton exchange.
TL;DR: In this article, the S-matrix in the gauge-fixed sigma model on AdS(5) x S-5 to the leading order in perturbation theory is analyzed.
Abstract: We calculate the S-matrix in the gauge-fixed sigma-model on AdS(5) x S-5 to the leading order in perturbation theory, and analyze how supersymmetry is realized on the scattering states. A mild nonlocality of the supercharges implies that their action on multi-particle states does not follow the Leibniz rule, which is replaced by a nontrivial coproduct. The plane wave symmetry algebra is thus naturally enhanced to a Hopf algebra. This structure mirrors that of the large't Hooft coupling expansion of the S-matrix for the spin chain in the dual super-Yang-Mills theory.
TL;DR: In this article, the authors studied the thermodynamics of massive = 2 supersymmetric hypermultiplets coupled to = 4 SU(Nc) Yang-Mills theory in the limits of large Nc and large 't Hooft coupling at finite baryon number density.
Abstract: We use the AdS/CFT correspondence to study the thermodynamics of massive = 2 supersymmetric hypermultiplets coupled to = 4 supersymmetric SU(Nc) Yang-Mills theory in the limits of large Nc and large 't Hooft coupling. In particular, we study the theory at finite baryon number density. At zero temperature, we present an exact expression for the hypermultiplets' leading-order contribution to the free energy, and in the supergravity description we clarify which D-brane configuration is appropriate for any given value of the chemical potential. We find a second-order phase transition when the chemical potential equals the mass. At finite temperature, we present an exact expression for the hypermultiplets' leading-order contribution to the free energy at zero mass.
TL;DR: In this article, the conductivity tensor of a probe D7-brane was derived for a supersymmetric hyper-multiplet field at finite baryon density, propagating through Yang-Mills plasma.
Abstract: We use the AdS/CFT correspondence to compute a conductivity associated with massive $\mathcal{N}=2$ supersymmetric hypermultiplet fields at finite baryon density, propagating through an $\mathcal{N}=4$ supersymmetric $SU({N}_{c})$ Yang-Mills plasma in the large ${N}_{c}$, large 't Hooft coupling limit. We do so by introducing external electric and magnetic fields coupled to baryon number and computing the resulting induced current, from which we extract the conductivity tensor. At large hypermultiplet mass we compute the drag force on the charge carriers. We also compute the product of the drag coefficient with the kinetic mass, and find that the answer is unchanged from the zero-density case. The gravitational dual is a probe D7-brane, with a nontrivial world volume gauge field configuration, in an AdS-Schwarzschild background. We identify an effective horizon on the D7-brane world volume analogous to the world sheet horizon observed for strings moving in the same background. We generalize our results to a class of theories described by probe D-branes in various backgrounds.
TL;DR: In this paper, the authors derived the one-loop energy of a folded string rotating with angular momenta in AdS 3 × S 1 ⊂ AdS 5 × S 5 in the limit 1 ≪ J ≪ S, z = λ log (S / J ) / ( π J ) fixed.
TL;DR: In this paper, the authors studied supergravity backgrounds encoded through the gauge/string correspondence by the SU(n) × SU(N) theory arising on N D3-branes on the conifold.
Abstract: We study supergravity backgrounds encoded through the gauge/string correspondence by the SU(N) × SU(N) theory arising on N D3-branes on the conifold. As discussed in hep-th/9905104, the dynamics of this theory describes warped versions of both the singular and the resolved conifolds through different (symmetry breaking) vacua. We construct these supergravity solutions explicitly and match them with the gauge theory with different sets of vacuum expectation values of the bi-fundamental fields A1,A2,B1,B2. For the resolved conifold, we find a non-singular SU(2) × U(1) × U(1) symmetric warped solution produced by a stack of D3-branes localized at a point on the blown-up 2-sphere. It describes a smooth RG flow from AdS5 × T1,1 in the UV to AdS5 × S5 in the IR, produced by giving a VEV to just one field, e.g. B2. The presence of a condensate of baryonic operator detB2 is confirmed using a Euclidean D3-brane wrapping a 4-cycle inside the resolved conifold. The Green's functions on the singular and resolved conifolds are central to our calculations and are discussed in some detail.
TL;DR: In this paper, a generalization of the AdS/CFT conjecture postulates a duality between IIA string theory and 16 supercharge Yang-Mills quantum mechanics in the large N 't Hooft limit.
Abstract: A generalization of the AdS/CFT conjecture postulates a duality between IIA string theory and 16 supercharge Yang-Mills quantum mechanics in the large N 't Hooft limit. At low temperatures string theory describes black holes, whose thermodynamics may hence be studied using the dual quantum mechanics. This quantum mechanics is strongly coupled which motivates the use of lattice techniques. We argue that, contrary to expectation, the theory when discretized naively will nevertheless recover continuum supersymmetry as the lattice spacing is sent to zero. We test these ideas by studying the 4 supercharge version of this Yang-Mills quantum mechanics in the 't Hooft limit. We use both a naive lattice action and a manifestly supersymmetric action. Using Monte Carlo methods we simulate the Euclidean theories, and study the lattice continuum limit, for both thermal and non-thermal periodic boundary conditions, confirming continuum supersymmetry is recovered for the naive action when appropriate. We obtain results for the thermal system with N up to 12. These favor the existence of a single deconfined phase for all non-zero temperatures. These results are an encouraging indication that the 16 supercharge theory is within reach using similar methods and resources.