Showing papers on "AdS/CFT correspondence published in 2014"

Black holes and the butterfly effect

Abstract: We use holography to study sensitive dependence on initial conditions in strongly coupled field theories. Specifically, we mildly perturb a thermofield double state by adding a small number of quanta on one side. If these quanta are released a scrambling time in the past, they destroy the local two-sided correlations present in the unperturbed state. The corresponding bulk geometry is a two-sided AdS black hole, and the key effect is the blueshift of the early infalling quanta relative to the t = 0 slice, creating a shock wave. We comment on string- and Planck-scale corrections to this setup, and discuss points that may be relevant to the firewall controversy.

Gauge/String Duality, Hot QCD and Heavy Ion Collisions

Abstract: 1. Opening remarks 2. A heavy ion phenomenology primer 3. Results from lattice QCD at nonzero temperature 4. Introducing the gauge/string duality 5. A duality toolbox 6. Bulk properties of strongly coupled plasma 7. From hydrodynamics for far-from-equilibrium dynamics 8. Probing strongly coupled plasma 9. Quarkonium mesons in strongly coupled plasma 10. Concluding remarks and outlook Appendixes References Index.

Gravitation from entanglement in holographic CFTs

Abstract: Entanglement entropy obeys a ‘first law’, an exact quantum generalization of the ordinary first law of thermodynamics. In any CFT with a semiclassical holographic dual, this first law has an interpretation in the dual gravitational theory as a constraint on the spacetimes dual to CFT states. For small perturbations around the CFT vacuum state, we show that the set of such constraints for all ball-shaped spatial regions in the CFT is exactly equivalent to the requirement that the dual geometry satisfy the gravitational equations of motion, linearized about pure AdS. For theories with entanglement entropy computed by the Ryu-Takayanagi formula S = $ \mathcal{A} $ /(4G N), we obtain the linearized Einstein equations. For theories in which the vacuum entanglement entropy for a ball is computed by more general Wald functionals, we obtain the linearized equations for the associated higher-curvature theories. Using the first law, we also derive the holographic dictionary for the stress tensor, given the holographic formula for entanglement entropy. This method provides a simple alternative to holographic renormalization for computing the stress tensor expectation value in arbitrary higher derivative gravitational theories.

Maximin Surfaces, and the Strong Subadditivity of the Covariant Holographic Entanglement Entropy

Abstract: The covariant holographic entropy conjecture of AdS/CFT relates the entropy of a boundary region R to the area of an extremal surface in the bulk spacetime. This extremal surface can be obtained by a maximin construction, allowing many new results to be proven. On manifolds obeying the null curvature condition, these extremal surfaces: (i) always lie outside the causal wedge of R, (ii) have less area than the bifurcation surface of the causal wedge, (iii) move away from the boundary as R grows, and (iv) obey strong subadditivity and monogamy of mutual information. These results suggest that the information in R allows the bulk to be reconstructed all the way up to the extremal area surface. The maximin surfaces are shown to exist on spacetimes without horizons, and on black hole spacetimes with Kasner-like singularities.

Bulk Locality and Quantum Error Correction in AdS/CFT

Abstract: We point out a connection between the emergence of bulk locality in AdS/CFT and the theory of quantum error correction. Bulk notions such as Bogoliubov transformations, location in the radial direction, and the holographic entropy bound all have natural CFT interpretations in the language of quantum error correction. We also show that the question of whether bulk operator reconstruction works only in the causal wedge or all the way to the extremal surface is related to the question of whether or not the quantum error correcting code realized by AdS/CFT is also a "quantum secret sharing scheme", and suggest a tensor network calculation that may settle the issue. Interestingly, the version of quantum error correction which is best suited to our analysis is the somewhat nonstandard "operator algebra quantum error correction" of Beny, Kempf, and Kribs. Our proposal gives a precise formulation of the idea of "subregion-subregion" duality in AdS/CFT, and clarifies the limits of its validity.

A simple holographic model of momentum relaxation

Abstract: We consider a holographic model consisting of Einstein-Maxwell theory in d + 1 bulk spacetime dimensions with d 1 massless scalarelds. Momentum relaxation is realised simply through spatially dependent sources for operators dual to the neutral scalars, which can be engineered so that the bulk stress tensor and resulting black brane geometry are homogeneous and isotropic. We analytically calculate the DC conductivity, which isnite. In the d = 3 case, both the black hole geometry and shear-mode current- current correlators are those of a sector of massive gravity.

Universality of Long-Distance AdS Physics from the CFT Bootstrap

Abstract: We begin by explicating a recent proof of the cluster decomposition principle in AdS�4 from the CFT�3 bootstrap. The CFT argument also computes the leading interactions between distant objects in AdS�4, and we conrm the universal agreement between the CFT bootstrap and AdS gravity in the semi-classical limit. We proceed to study the generalization to CFT2, which requires knowledge of the Virasoro conformal blocks in a lightcone OPE limit. We compute these blocks in a semi- classical, large central charge approximation, and use them to prove a suitably modied theorem. In particular, from the d = 2 bootstrap we prove the existence of large spin operators withxedanomalous dimensions' indicative of the presence of decit angles in AdS3. As we approach the threshold for the BTZ black hole, interpreted as a CFT2 scaling dimension, the twist spectrum of large spin operators becomes dense. Due to the exchange of the Virasoro identity block, primary states above the BTZ threshold mimic a thermal background for light operators. We derive the BTZ quasi- normal modes, and we use the bootstrap equation to prove that the twist spectrum is dense. Corrections to thermality could be obtained from a more rened computation of the Virasoro conformal blocks.

Universal spectrum of 2d conformal field theory in the large c limit

Abstract: Two-dimensional conformal eld theories exhibit a universal free energy in the high temperature limit T ! 1, and a universal spectrum in the Cardy regime, ! 1. We show that a much stronger form of universality holds in theories with a large central charge c and a sparse light spectrum. In these theories, the free energy is universal at all values of the temperature, and the microscopic spectrum matches the Cardy entropy for all c . The same is true of three-dimensional quantum gravity; therefore our results provide simple necessary and sucient criteria for 2d CFTs to behave holographically in terms of the leading spectrum and thermodynamics. We also discuss several applications to CFT and gravity, including operator dimension bounds derived from the modular bootstrap, universality in symmetric orbifolds, and the role of non-universal ‘enigma’ saddlepoints in the thermodynamics of 3d gravity.

Holographic entanglement entropy for general higher derivative gravity

Abstract: We propose a general formula for calculating the entanglement entropy in theories dual to higher derivative gravity where the Lagrangian is a contraction of Riemann tensors. Our formula consists of Wald’s formula for the black hole entropy, as well as corrections involving the extrinsic curvature. We derive these corrections by noting that they arise from naively higher order contributions to the action which are enhanced due to would-be logarithmic divergences. Our formula reproduces the Jacobson-Myers entropy in the context of Lovelock gravity, and agrees with existing results for general four-derivative gravity. We emphasize that the formula should be evaluated on a particular bulk surface whose location can in principle be determined by solving the equations of motion with conical boundary conditions. This may be difficult in practice, and an alternative method is desirable. A natural prescription is simply minimizing our formula, analogous to the Ryu-Takayanagi prescription for Einstein gravity. We show that this is correct in several examples including Lovelock and general four-derivative gravity.

Gravitational dynamics from entanglement 'thermodynamics'

Abstract: In a general conformal field theory, perturbations to the vacuum state obey the relation δS = δE, where δS is the change in entanglement entropy of an arbitrary ball-shaped region, and δE is the change in “hyperbolic” energy of this region. In this note, we show that for holographic conformal field theories, this relation, together with the holographic connection between entanglement entropies and areas of extremal surfaces and the standard connection between the field theory stress tensor and the boundary behavior of the metric, implies that geometry dual to the perturbed state satisfies Einstein’s equations expanded to linear order about pure AdS.

Holographic Q-lattices

Abstract: We introduce a new framework for constructing black hole solutions that are holographically dual to strongly coupled field theories with explicitly broken translation invariance. Using a classical gravitational theory with a continuous global symmetry leads to constructions that involve solving ODEs instead of PDEs. We study in detail D = 4 Einstein-Maxwell theory coupled to a complex scalar field with a simple mass term. We construct black holes dual to metallic phases which exhibit a Drude-type peak in the optical conductivity, but there is no evidence of an intermediate scaling that has been reported in other holographic lattice constructions. We also construct black holes dual to insulating phases which exhibit a suppression of spectral weight at low frequencies. We show that the model also admits a novel AdS 3 × $ \mathbb{R} $ solution.

Thermoelectric DC conductivities from black hole horizons

Abstract: An analytic expression for the DC electrical conductivity in terms of black hole horizon data was recently obtained for a class of holographic black holes exhibiting momentum dissipation. We generalise this result to obtain analogous expressions for the DC thermoelectric and thermal conductivities. We illustrate our results using some holographic Q-lattice black holes as well as for some black holes with linear massless axions, in both D = 4 and D = 5 bulk spacetime dimensions, which include both spatially isotropic and anisotropic examples. We show that some recently constructed ground states of holographic Q-lattices, which can be either electrically insulating or metallic, are all thermal insulators.

State-dependent bulk-boundary maps and black hole complementarity

Abstract: We provide a simple and explicit construction of local bulk operators that describe the interior of a black hole in the AdS/CFT correspondence. The existence of these operators is predicated on the assumption that the mapping of CFT operators to local bulk operators depends on the state of the CFT. We show that our construction leads to an exactly local effective field theory in the bulk. Barring the fact that their charge and energy can be measured at infinity, we show that the commutator of local operators inside and outside the black hole vanishes exactly, when evaluated within correlation functions of the CFT. Our construction leads to a natural resolution of the strong subadditivity paradox of Mathur and Almheiri et al. Furthermore, we show how, using these operators, it is possible to reconcile small corrections to effective field theory correlators with the unitarity of black hole evaporation. We address and resolve all other arguments, advanced in A. Almheiri et al. J. High Energy Phys. 09 (2013) 018 and D. Marolf and J. Polchinski, Phys. Rev. Lett. 111, 171301 (2013), in favor of structure at the black hole horizon. We extend our construction to states that are near equilibrium, and thereby also address the ``frozen vacuum'' objections of R. Bousso, Phys. Rev. Lett. 112, 041102 (2014). Finally, we explore an intriguing link between our construction of interior operators and Tomita-Takesaki theory.

Novel metals and insulators from holography

Abstract: Using simple holographic models in D = 4 spacetime dimensions we construct black hole solutions dual to d = 3 CFTs at finite charge density with a Q-lattice deformation. At zero temperature we find new ground state solutions, associated with broken translation invariance in either one or both spatial directions, which exhibit insulating or metallic behaviour depending on the parameters of the holographic theory. For low temperatures and small frequencies, the real part of the optical conductivity exhibits a power-law behaviour. We also obtain an expression for the the DC conductivity at finite temperature in terms of horizon data of the black hole solutions.

Generalized entropy and higher derivative gravity

Abstract: We derive an extension of the Ryu-Takayanagi prescription for curvature squared theories of gravity in the bulk, and comment on a prescription for more general theories. This results in a new entangling functional, that contains a correction to Wald’s entropy. The new term is quadratic in the extrinsic curvature. The coefficient of this correction is a second derivative of the lagrangian with respect to the Riemann tensor. For Gauss-Bonnet gravity, the new functional reduces to Jacobson-Myers’.

Boundary Stress-Energy Tensor and Newton-Cartan Geometry in Lifshitz Holography

Abstract: For a specific action supporting z = 2 Lifshitz geometries we identify the Lifshitz UV completion by solving for the most general solution near the Lifshitz boundary. We identify all the sources as leading components of bulk fields which requires a vielbein formalism. This includes two linear combinations of the bulk gauge field and timelike vielbein where one asymptotes to the boundary timelike vielbein and the other to the boundary gauge field. The geometry induced from the bulk onto the boundary is a novel extension of Newton-Cartan geometry that we call torsional Newton-Cartan (TNC) geometry. There is a constraint on the sources but its pairing with a Ward identity allows one to reduce the variation of the on-shell action to unconstrained sources. We compute all the vevs along with their Ward identities and derive conditions for the boundary theory to admit conserved currents obtained by contracting the boundary stress-energy tensor with a TNC analogue of a conformal Killing vector. We also obtain the anisotropic Weyl anomaly that takes the form of a Hořava-Lifshitz action defined on a TNC geometry. The Fefferman-Graham expansion contains a free function that does not appear in the variation of the on-shell action. We show that this is related to an irrelevant deformation that selects between two different UV completions.

Jordanian deformations of the AdS5 × S5 superstring

Abstract: We consider Jordanian deformations of the AdS5 × S5 superstring action. These deformations correspond to non-standard q-deformations. In particular, it is possible to perform a partial deformation, for example, of the AdS5 part only, or of the S5 part only. Then the classical action and the Lax pair are constructed with a linear, twisted and extended R operator. It is shown that the action preserves the κ-symmetry.

Spinning AdS propagators

Abstract: 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 find a split representation for the bulk-to-bulk propagator, by writing it as an integral over the boundary of the product of two bulk-to-boundary propagators. We exemplify the use of this representation with the computation of the conformal partial wave decomposition of Witten diagrams. In particular, we determine the Mellin amplitude associated to AdS graviton exchange between minimally coupled scalars of general dimension, including the regular part of the amplitude.

Holography for (1,0) theories in six dimensions

Abstract: M-theory and string theory predict the existence of many six-dimensional SCFTs. In particular, type IIA brane constructions involving NS5-, D6- and D8-branes conjecturally give rise to a very large class ofN = (1; 0) CFTs in six dimensions. We point out that these theories sit at the end of RG ows which start from six-dimensional theories which admit an M-theory construction as a M5 stack transverse to R 4 =Zk R. The ows are triggered by Higgs branch expectation values and correspond to D6’s opening up into transverse D8-branes via a Nahm pole. We nd a precise correspondence between these

The N=8 superconformal bootstrap in three dimensions

Abstract: We analyze the constraints imposed by unitarity and crossing symmetry on the four-point function of the stress-tensor multiplet of $$ \mathcal{N}=8 $$ superconformal field theories in three dimensions. We first derive the superconformal blocks by analyzing the superconformal Ward identity. Our results imply that the OPE of the primary operator of the stress-tensor multiplet with itself must have parity symmetry. We then analyze the relations between the crossing equations, and we find that these equations are mostly redundant. We implement the independent crossing constraints numerically and find bounds on OPE coefficients and operator dimensions as a function of the stress-tensor central charge. To make contact with known $$ \mathcal{N}=8 $$ superconformal field theories, we compute this central charge in a few particular cases using supersymmetric localization. For limiting values of the central charge, our numerical bounds are nearly saturated by the large N limit of ABJM theory and also by the free U(1) × U(1) ABJM theory.

Integrable deformations of strings on symmetric spaces

Abstract: A general class of deformations of integrable sigma-models with symmetric space F=G target-spaces are found. These deformations involve dening the non-abelian T dual of the sigma-model and then replacing the coupling of the Lagrange multiplier imposing atness with a gauged F=F WZW model. The original sigma-model is obtained in the limit of large level. The resulting deformed theories are shown to preserve both integrability and the equations-of-motion, but involve a deformation of the symplectic structure. It is shown that this deformed symplectic structure involves a linear combination of the original Poisson bracket and a generalization of the Faddeev-Reshetikhin Poisson bracket which we show can be re-expressed as two decoupled F current algebras. It is then shown that the deformation can be incorporated into the classical model of strings on RF=G via a generalization of the Pohlmeyer reduction. In this case, in the limit of large sigma-model coupling it is shown that the theory becomes the relativistic symmetric space sine-Gordon theory. These results point to the existence of a deformation of this kind for the full Green-Schwarz superstring on AdS5�S 5 .

A theory of first order dissipative superfluid dynamics

Abstract: We determine the most general form of the equations of relativistic superfluid hydrodynamics consistent with Lorentz invariance, time-reversal invariance, the Onsager principle and the second law of thermodynamics at first order in the derivative expansion. Once parity is violated, either because the U(1) symmetry is anomalous or as a consequence of a different parity-breaking mechanism, our results deviate from the standard textbook analysis of superfluids. Our general equations require the specification of twenty parameters (such as the viscosity and conductivity). In the limit of small relative superfluid velocities we find a seven parameter set of equations. In the same limit, we have used the AdS/CFT correspondence to compute the parity odd contributions to the superfluid equations of motion for a generic holographic model and have verified that our results are consistent.

Exact results for five-dimensional superconformal field theories with gravity duals

Abstract: We apply the technique of supersymmetric localization to exactly compute the S 5 partition function of several large N superconformal field theories in five dimensions that have AdS6 duals in massive type IIA supergravity. The localization computations are performed in the non-renormalizable effective field theories obtained through relevant deformations of the UV superconformal field theories. We compare the S 5 free energy to a holographic computation of entanglement entropy in the AdS6 duals and find perfect agreement. In particular, we reproduce the N 5/2 scaling of the S 5 free energy that was expected from supergravity.

Black Hole Interior in the Holographic Correspondence and the Information Paradox

Abstract: We show that, within the AdS/CFT correspondence, recent formulations of the information paradox can be reduced to a question about the existence of certain kinds of operators in the conformal field theory (CFT). We describe a remarkably simple construction of these operators on a given state of the CFT. Our construction leads to a smooth horizon, addresses the strong subadditivity paradox, while preserving locality within effective field theory, and reconciles the existence of the interior with the growth of states with energy in the CFT. We also extend our construction to nonequilibrium states.

Holographic thermalization, stability of anti-de sitter space, and the Fermi-Pasta-Ulam paradox.

Abstract: For a real massless scalar field in general relativity with a negative cosmological constant, we uncover a large class of spherically symmetric initial conditions that are close to anti--de Sitter space (AdS) but whose numerical evolution does not result in black hole formation. According to the AdS/conformal field theory (CFT) dictionary, these bulk solutions are dual to states of a strongly interacting boundary CFT that fail to thermalize at late times. Furthermore, as these states are not stationary, they define dynamical CFT configurations that do not equilibrate. We develop a two-time-scale perturbative formalism that captures both direct and inverse cascades of energy and agrees with our fully nonlinear evolutions in the appropriate regime. We also show that this formalism admits a large class of quasiperiodic solutions. Finally, we demonstrate a striking parallel between the dynamics of AdS and the classic Fermi-Pasta-Ulam-Tsingou problem.

Higher spins in AdS5 at one loop: vacuum energy, boundary conformal anomalies and AdS/CFT

Abstract: We consider general-symmetry higher spin fields in AdS5 and derive the expressions for their one-loop corrections to vacuum energy E c and the associated 4d boundary conformal anomaly a-coefficient. We propose a similar expression for the second conformal anomaly c-coefficient. We show that all the three quantities (E c , a, c) computed for $$ \mathcal{N}=8 $$ gauged 5d supergravity are equal to $$ -\frac{1}{2} $$ of their values for $$ \mathcal{N}=4 $$ conformal 4d supergravity and also to twice the values for $$ \mathcal{N}=4 $$ Maxwell multiplet. This gives a 5d derivation of the fact that the system of $$ \mathcal{N}=4 $$ conformal supergravity and four $$ \mathcal{N}=4 $$ Maxwell multiplets is anomaly free. The values of (E c , a, c) for the states at level p of Kaluza-Klein tower of 10d type IIB supergravity compactified on S 5 turn out to be equal to those for p copies of $$ \mathcal{N}=4 $$ Maxwell multiplets. This may be related to the fact that these states appear in the tensor product of p superdoubletons. Under a natural regularization of the sum over p, the full 10d supergravity contribution is then minus that of one Maxwell multiplet, in agreement with the standard adjoint AdS/CFT duality (SU(N) SYM contribution is N 2 − 1 times that of one Maxwell multiplet). We also verify the matching of (E c , a, c) for spin 0 and $$ \frac{1}{2} $$ boundary theory cases of vectorial AdS/CFT duality. The consistency conditions for vectorial AdS/CFT turn out to be equivalent to the cancellation of anomalies in the closely related 4d conformal higher spin theories. In addition, we study novel example of the vectorial AdS/CFT duality when the boundary theory is described by free spin 1 fields and is dual to a particular higher spin theory in AdS5 containing fields in mixed-symmetry representations. We also discuss its supersymmetric generalizations.

Multiboundary Wormholes and Holographic Entanglement

Abstract: The AdS/CFT correspondence relates quantum entanglement between boundary conformal field theories and geometric connections in the dual asymptotically anti-de Sitter spacetime. We consider entangled states in the $n$-fold tensor product of a 1 + 1 dimensional CFT Hilbert space defined by the Euclidean path integral over a Riemann surface with n holes. In one region of moduli space, the dual bulk state is a black hole with n asymptotically AdS3 regions connected by a common wormhole, while in other regions the bulk fragments into disconnected components. We study the entanglement structure and compute the wave function explicitly in the puncture limit of the Riemann surface in terms of CFT n-point functions. We also use AdS minimal surfaces to measure entanglement more generally. In some regions of the moduli space the entanglement is entirely multipartite, though not of the GHZ type. However, even when the bulk is completely connected, there are regions of the moduli space in which the entanglement is instead almost entirely bipartite: significant entanglement occurs only between pairs of CFTs. We develop new tools to analyze intrinsically n-partite entanglement, and use these to show that for some wormholes with n similar sized horizons there is intrinsic entanglement between all n parties, and that the distillable entanglement between the asymptotic regions is at least $(n+1)/2$ partite.

Lunin-Maldacena backgrounds from the classical Yang-Baxter equation — towards the gravity/CYBE correspondence

Abstract: We consider γ-deformations of the AdS5×S5 superstring as Yang-Baxter sigma models with classical r-matrices satisfying the classical Yang-Baxter equation (CYBE). An essential point is that the classical r-matrices are composed of Cartan generators only and then generate abelian twists. We present examples of the r-matrices that lead to real γ-deformations of the AdS5×S5 superstring. Finally we discuss a possible classification of integrable deformations and the corresponding gravity solution in terms of solutions of CYBE. This classification may be called the gravity/CYBE correspondence.

Thermo-electric transport in gauge/gravity models with momentum dissipation

Abstract: We present a systematic definition and analysis of the thermo-electric linear response in gauge/gravity systems focusing especially on models with massive gravity in the bulk and therefore momentum dissipation in the dual field theory. A precise treatment of finite counter-terms proves to be essential to yield a consistent physical picture whose hydrodynamic and beyond-hydrodynamics behaviors noticeably match with field theoretical expectations. The model furnishes a possible gauge/gravity description of the crossover from the quantum-critical to the disorder-dominated Fermi-liquid behaviors, as expected in graphene.

Twist operators in higher dimensions

Abstract: We study twist operators in higher dimensional CFT’s. In particular, we express their conformal dimension in terms of the energy density for the CFT in a particular thermal ensemble. We construct an expansion of the conformal dimension in power series around n =1, with n being replica parameter. We show that the coefficients in this expansion are determined by higher point correlations of the energy-momentum tensor. In particular, the first and second terms, i.e. the first and second derivatives of the scaling dimension, have a simple universal form. We test these results using holography and free field theory computations, finding agreement in both cases. We also consider the ‘operator product expansion’ of spherical twist operators and finally, we examine the behaviour of correlators of twist operators with other operators in the limit n → 1.