Showing papers on "AdS/CFT correspondence published in 2013"

Quantum corrections to holographic entanglement entropy

Abstract: We consider entanglement entropy in quantum field theories with a gravity dual. In the gravity description, the leading order contribution comes from the area of a minimal surface, as proposed by Ryu-Takayanagi. Here we describe the one loop correction to this formula. The minimal surface divides the bulk into two regions. The bulk loop correction is essentially given by the bulk entanglement entropy between these two bulk regions. We perform some simple checks of this proposal.

Convexity and Liberation at Large Spin

Abstract: We consider several aspects of unitary higher-dimensional conformal field theories (CFTs). We first study massive deformations that trigger a flow to a gapped phase. Deep inelastic scattering in the gapped phase leads to a convexity property of dimensions of spinning operators of the original CFT. We further investigate the dimensions of spinning operators via the crossing equations in the light-cone limit. We find that, in a sense, CFTs become free at large spin and 1/s is a weak coupling parameter. The spectrum of CFTs enjoys additivity: if two twists τ 1, τ 2 appear in the spectrum, there are operators whose twists are arbitrarily close to τ 1 + τ 2. We characterize how τ 1 + τ 2 is approached at large spin by solving the crossing equations analytically. We find the precise form of the leading correction, including the prefactor. We compare with examples where these observables were computed in perturbation theory, or via gauge-gravity duality, and find complete agreement. The crossing equations show that certain operators have a convex spectrum in twist space. We also observe a connection between convexity and the ratio of dimension to charge. Applications include the 3d Ising model, theories with a gravity dual, SCFTs, and patterns of higher spin symmetry breaking.

Black holes in three dimensional higher spin gravity: a review

Abstract: We review recent progress in the construction of black holes in three dimensional higher spin gravity theories. Starting from spin-3 gravity and working our way toward the theory of an infinite tower of higher spins coupled to matter, we show how to harness higher spin gauge invariance to consistently generalize familiar notions of black holes. We review the construction of black holes with conserved higher spin charges and the computation of their partition functions to leading asymptotic order. In view of the anti-de Sitter/conformal field theory (CFT) correspondence as applied to certain vector-like conformal field theories with extended conformal symmetry, we successfully compare to CFT calculations in a generalized Cardy regime. A brief recollection of pertinent aspects of ordinary gravity is also given.This article is part of a special issue of Journal of Physics A: Mathematical and Theoretical devoted to ‘Higher spin theories and holography’.

Constraining conformal field theories with a slightly broken higher spin symmetry

Abstract: We consider three-dimensional conformal field theories that have a higher spin symmetry that is slightly broken. The theories have a large-N limit in the sense that the operators separate into single trace and multitrace and obey the usual large-N factorization properties. We assume that the spectrum of single trace operators is similar to the one that one obtains in the Vasiliev theories. Namely the only single trace operators are the higher spin currents plus an additional scalar. The anomalous dimensions of the higher spin currents are of the order 1/N. Using the slightly broken higher spin symmetry, we constrain the three-point functions of the theories to a leading order in N. We show that there are two families of solutions. One family can be realized as a theory of N fermions with an O(N) Chern?Simons gauge field, the other as an N bosons plus the Chern?Simons gauge field. The family of solutions is parametrized by the 't Hooft coupling. At special parity preserving points, we obtain the critical O(N) models: the Wilson?Fisher one and the Gross?Neveu one. Our analysis also fixes the on-shell three-point functions of Vasiliev's theory on AdS4 or dS4.

Two-dimensional SCFTs from wrapped branes and c-extremization

Abstract: We apply c-extremization [1], whose proof we review in full detail, to study twodimensional $ \mathcal{N} $ = (0, 2) superconformal field theories arising from the low-energy dynamics of D3-branes wrapped on Riemann surfaces and M5-branes wrapped on four-manifolds We compute the exact central charges of these theories using anomalies and c-extremization In all cases we also construct AdS3 supergravity solutions of type IIB and eleven-dimensional supergravity, which are holographic duals to the field theories at large N, and exactly reproduce the central charges computed via c-extremization

Holography of 3d Flat Cosmological Horizons

Abstract: We provide a first derivation of the Bekenstein-Hawking entropy of 3D flat cosmological horizons in terms of the counting of states in a dual field theory. These horizons appear in the flat limit of nonextremal rotating Banados-Teitleboim-Zanelli black holes and are remnants of the inner horizons. They also satisfy the first law of thermodynamics. We study flat holography as a limit of ${\mathrm{AdS}}_{3}/{\mathrm{CFT}}_{2}$ to semiclassically compute the density of states in the dual theory, which is given by a contraction of a 2D conformal field theory, exactly reproducing the bulk entropy in the limit of large charges. We comment on how the dual theory reproduces the bulk first law and how cosmological bulk excitations are matched with boundary quantum numbers.

Entanglement temperature and entanglement entropy of excited states

Abstract: We derive a general relation between the ground state entanglement Hamiltonian and the physical stress tensor within the path integral formalism. For spherical entangling surfaces in a CFT, we reproduce the local ground state entanglement Hamiltonian derived by Casini, Huerta and Myers. The resulting reduced density matrix can be characterized by a spatially varying “entanglement temperature”. Using the entanglement Hamiltonian, we calculate the first order change in the entanglement entropy due to changes in conserved charges of the ground state, and find a local first law-like relation for the entanglement entropy. Our approach provides a field theory derivation and generalization of recent results obtained by holographic techniques. However, we note a discrepancy between our field theoretically derived results for the entanglement entropy of excited states with a non-uniform energy density and current holographic results in the literature. Finally, we give a CFT derivation of a set of constraint equations obeyed by the entanglement entropy of excited states in any dimension. Previously, these equations were derived in the context of holography.

Holographic local quenches and entanglement density

Abstract: We propose a free falling particle in an AdS space as a holographic model of local quench. Local quenches are triggered by local excitations in a given quantum system. We calculate the time-evolution of holographic entanglement entropy. We confirm a logarithmic time-evolution, which is known to be typical in two dimensional local quenches. To study the structure of quantum entanglement in general quantum systems, we introduce a new quantity which we call entanglement density and apply this analysis to quantum quenches. We show that this quantity is directly related to the energy density in a small size limit. Moreover, we find a simple relationship between the amount of quantum information possessed by a massive object and its total energy based on the AdS/CFT.

The Entanglement Renyi Entropies of Disjoint Intervals in AdS/CFT

Abstract: We study entanglement Renyi entropies (EREs) of 1+1 dimensional CFTs with classical gravity duals. Using the replica trick the EREs can be related to a partition function of n copies of the CFT glued together in a particular way along the intervals. In the case of two intervals this procedure defines a genus n-1 surface and our goal is to find smooth three dimensional gravitational solutions with this surface living at the boundary. We find two families of handlebody solutions labelled by the replica index n. These particular bulk solutions are distinguished by the fact that they do not spontaneously break the replica symmetries of the boundary surface. We show that the regularized classical action of these solutions is given in terms of a simple numerical prescription. If we assume that they give the dominant contribution to the gravity partition function we can relate this classical action to the EREs at leading order in G_N. We argue that the prescription can be formulated for non-integer n. Upon taking the limit n -> 1 the classical action reproduces the predictions of the Ryu-Takayanagi formula for the entanglement entropy.

Holographic entanglement beyond classical gravity

Abstract: The Renyi entropies and entanglement entropy of 1+1 CFTs with gravity duals can be computed by explicit construction of the bulk spacetimes dual to branched covers of the boundary geometry. At the classical level in the bulk this has recently been shown to reproduce the conjectured Ryu-Takayanagi formula for the holographic entanglement entropy. We study the one-loop bulk corrections to this formula. The functional determinants in the bulk geometries are given by a sum over certain words of generators of the Schottky group of the branched cover. For the case of two disjoint intervals on a line we obtain analytic answers for the one-loop entanglement entropy in an expansion in small cross-ratio. These reproduce and go beyond anticipated universal terms that are not visible classically in the bulk. We also consider the case of a single interval on a circle at finite temperature. At high temperatures we show that the one-loop contributions introduce expected finite size corrections to the entanglement entropy that are not present classically. At low temperatures, the one-loop corrections capture the mixed nature of the density matrix, also not visible classically below the Hawking-Page temperature.

One loop tests of higher spin AdS/CFT

Abstract: Vasiliev’s type A higher spin theories in AdS4 have been conjectured to be dual to the U(N) or O(N) singlet sectors in 3-d conformal field theories with N-component scalar fields. We compare the $ \mathcal{O} $ (N 0) correction to the 3-sphere free energy F in the CFTs with corresponding calculations in the higher spin theories. This requires evaluating a regularized sum over one loop vacuum energies of an infinite set of massless higher spin gauge fields in Euclidean AdS4. For the Vasiliev theory including fields of all integer spin and a scalar with Δ = 1 boundary condition, we show that the regularized sum vanishes. This is in perfect agreement with the vanishing of subleading corrections to F in the U(N) singlet sector of the theory of N free complex scalar fields. For the minimal Vasiliev theory including fields of only even spin, the regularized sum remarkably equals the value of F for one free real scalar field. This result may agree with the O(N) singlet sector of the theory of N real scalar fields, provided the coupling constant in the Vasiliev theory is identified as G N ~ 1/(N − 1). Similarly, consideration of the USp(N) singlet sector for N complex scalar fields, which we conjecture to be dual to the husp(2; 0|4) Vasiliev theory, requires G N ~ 1/(N + 1). We also test the higher spin AdS3 /CFT2 conjectures by calculating the regularized sum over one loop vacuum energies of higher spin fields in AdS3. We match the esult with the $ \mathcal{O} $ (N 0) term in the central charge of the W N minimal models; this requires a certain truncation of the CFT operator spectrum so that the bulk theory contains two real scalar fields with the same boundary conditions.

Wilson Lines and Entanglement Entropy in Higher Spin Gravity

Abstract: Holographic entanglement entropy provides a direct connection between classical geometry and quantum entanglement; however the usual prescription does not apply to theories of higher spin gravity, where standard notions of geometry are no longer gauge invariant. We present a proposal for the holographic computation of entanglement entropy in field theories dual to higher spin theories of gravity in AdS3. These theories have a Chern-Simons description, and our proposal involves a Wilson line in an infinite-dimensional representation of the bulk gauge group. In the case of spin−2 gravity such Wilson lines are the natural coupling of a heavy point particle to gravity and so are equivalent to the usual prescription of Ryu and Takayanagi. For higher spin gravity they provide a natural generalization of these ideas. We work out spin−3 gravity in detail, showing that our proposal recovers many expected results and computes thermal entropies of black holes with higher spin charge, finding agreement with previous expressions in the literature. We encounter some peculiarities in the case of non-unitary RG flow backgrounds and outline future generalizations.

Holographic superfluids and the dynamics of symmetry breaking.

Abstract: We explore the far-from-equilibrium response of a holographic superfluid using the AdS/CFT correspondence. We establish the dynamical phase diagram corresponding to quantum quenches of the order parameter source field. We find three distinct regimes of behavior that are related to the spectrum of black hole quasinormal modes. These correspond to damped oscillations of the order parameter and to overdamped approaches to the superfluid and normal states. The presence of three regimes, which includes an emergent dynamical temperature scale, is argued to occur more generally in time-reversal-invariant systems that display continuous symmetry breaking.

Entanglement entropy in de Sitter space

Abstract: We compute the entanglement entropy for some quantum field theories on de Sitter space. We consider a superhorizon size spherical surface that divides the spatial slice into two regions, with the field theory in the standard vacuum state. First, we study a free massive scalar field. Then, we consider a strongly coupled field theory with a gravity dual, computing the entanglement using the gravity solution. In even dimensions, the interesting piece of the entanglement entropy is proportional to the number of e-foldings that elapsed since the spherical region was inside the horizon. In odd dimensions it is contained in a certain finite piece. In both cases the entanglement captures the long range correlations produced by the expansion.

Holographic entanglement plateaux

Abstract: We consider the entanglement entropy for holographic field theories in finite volume. We show that the Araki-Lieb inequality is saturated for large enough subregions, implying that the thermal entropy can be recovered from the knowledge of the region and its complement. We observe that this actually is forced upon us in holographic settings due to non-trivial features of the causal wedges associated with a given boundary region. In the process, we present an infinite set of extremal surfaces in Schwarzschild-AdS geometry anchored on a given entangling surface. We also offer some speculations regarding the homology constraint required for computing holographic entanglement entropy.

Fully dynamical simulation of central nuclear collisions.

Abstract: We present a fully dynamical simulation of central nuclear collisions around midrapidity at LHC energies. Unlike previous treatments, we simulate all phases of the collision, including the equilibration of the system. For the simulation, we use numerical relativity solutions to anti–de Sitter space/conformal field theory for the preequilibrium stage, viscous hydrodynamics for the plasma equilibrium stage, and kinetic theory for the low-density hadronic stage. Our preequilibrium stage provides initial conditions for hydrodynamics, resulting in sizable radial flow. The resulting light particle spectra reproduce the measurements from the ALICE experiment at all transverse momenta.

New Boundary Conditions for AdS3

Abstract: New chiral boundary conditions are found for quantum gravity with matter on AdS3. The associated asymptotic symmetry group is generated by a single right-moving U(1) Kac-Moody-Virasoro algebra with $ {c_R}=\frac{{3\ell }}{2G } $ . The Kac-Moody zero mode generates global left-moving translations and equals, for a BTZ black hole, the sum of the total mass and spin. The level is positive about the global vacuum and negative in the black hole sector, corresponding to ergosphere formation. Realizations arising in Chern-Simons gravity and string theory are analyzed. The new boundary conditions are shown to naturally arise for warped AdS3 in the limit that the warp parameter is taken to zero.

Exact higher-spin symmetry in CFT: all correlators in unbroken Vasiliev theory

Abstract: All correlation functions of conserved currents of the CFT that is dual to unbroken Vasiliev theory are found as invariants of higher-spin symmetry in the bulk of AdS. The conformal and higher-spin symmetry of the correlators as well as the conservation of currents are manifest, which also provides a direct link between the Maldacena-Zhiboedov result and higher-spin symmetries. Our method is in the spirit of AdS/CFT, though we never take any boundary limit or compute any bulk integrals. Boundary-to-bulk propagators are shown to exhibit an algebraic structure, living at the boundary of SpH(4), semidirect product of Sp(4) and the Heisenberg group. N-point correlation function is given by a product of N elements.

Dynamics of Entanglement Entropy from Einstein Equation

Abstract: We study the dynamics of entanglement entropy for weakly excited states in conformal field theories by using anti-de Sitter/conformal field theory (AdS/CFT). This is aimed at a first step to finding a counterpart of the Einstein equation in CFT language. In particular, we point out that the entanglement entropy satisfies differential equations that directly correspond to the Einstein equation in several setups of AdS/CFT. We also define a quantity called entanglement density in higher dimensional field theories and study its dynamical property for weakly excited states in conformal field theories.

Holographic charged Rényi entropies

Abstract: We construct a new class of entanglement measures by extending the usual definition of Renyi entropy to include a chemical potential. These charged Renyi entropies measure the degree of entanglement in different charge sectors of the theory and are given by Euclidean path integrals with the insertion of a Wilson line encircling the entangling surface. We compute these entropies for a spherical entangling surface in CFT’s with holographic duals, where they are related to entropies of charged black holes with hyperbolic horizons. We also compute charged Renyi entropies in free field theories.

AdS field theory from conformal field theory

Abstract: We provide necessary and sufficient conditions for a Conformal Field Theory to have a description in terms of a perturbative Effective Field Theory in AdS. The first two conditions are well-known: the existence of a perturbative ‘1/N ’ expansion and an approximate Fock space of states generated by a finite number of low-dimension operators. We add a third condition, that the Mellin amplitudes of the CFT correlators must be well- approximated by functions that are bounded by a polynomial at infinity in Mellin space, or in other words, that the Mellin amplitudes have an effective theory-type expansion. We explain the relationship between our conditions and unitarity, and provide an analogy with scattering amplitudes that becomes exact in the flat space limit of AdS. The analysis also yields a simple connection between conformal blocks and AdS diagrams, providing a new calculational tool very much in the spirit of the S-Matrix program. We also begin to explore the potential pathologies associated with higher spin fields in AdS by generalizing Weinberg’s soft theorems to AdS/CFT. The AdS analog of Weinberg’s argument constrains the interactions of conserved currents in CFTs, but there are potential loopholes that are unavailable to theories of massless higher spin particles in flat spacetime.

Membrane instantons from a semiclassical TBA

Abstract: The partition function on the three-sphere of ABJM theory contains non-perturbative corrections which correspond to membrane instantons in M-theory. These corrections can be studied in the Fermi gas approach to the partition function, and they are encoded in a system of integral equations of the TBA type. We study a semiclassical or WKB expansion of this TBA system in the ABJM coupling k, which corresponds to the strong coupling expansion of the type IIA string. This allows us to study membrane instanton corrections in M-theory at high order in the WKB expansion. Using these WKB results, we verify the conjectures for the form of the one-instanton correction at finite k proposed recently by Hatsuda, Moriyama and Okuyama (HMO), which are in turn based on a conjectural cancellation of divergences between worldsheet instantons and membrane instantons. The HMO cancellation mechanism is important since it shows in a precise, quantitative way, that the perturbative genus expansion is radically insufficient at strong coupling, and that non-perturbative membrane effects are essential to make sense of the theory. We propose analytic expressions in k for the full two-membrane instanton correction and for higher-order non-perturbative terms, which pass many consistency checks and provide further evidence for the HMO mechanism.

Exact holographic mapping and emergent space-time geometry

Abstract: In this paper, we propose an {\it exact holographic mapping} which is a unitary mapping from the Hilbert space of a lattice system in flat space (boundary) to that of another lattice system in one higher dimension (bulk). By defining the distance in the bulk system from two-point correlation functions, we obtain an emergent bulk space-time geometry that is determined by the boundary state and the mapping. As a specific example, we study the exact holographic mapping for $(1+1)$-dimensional lattice Dirac fermions and explore the emergent bulk geometry corresponding to different boundary states including massless and massive states at zero temperature, and the massless system at finite temperature. We also study two entangled one-dimensional chains and show that the corresponding bulk geometry consists of two asymptotic regions connected by a worm-hole. The quantum quench of the coupled chains is mapped to dynamics of the worm-hole. In the end we discuss the general procedure of applying this approach to interacting systems, and other open questions.

AdS Description of Induced Higher-Spin Gauge Theory

Abstract: We study deformations of three-dimensional large N CFTs by double-trace operators constructed from spin s single-trace operators of dimension Δ. These theories possess UV fixed points, and we calculate the change of the 3-sphere free energy δF = F UV − F IR. To describe the UV fixed point using the dual AdS4 space we modify the boundary conditions on the spin s field in the bulk; this approach produces δF in agreement with the field theory calculations. If the spin s operator is a conserved current, then the fixed point is described by an induced parity invariant conformal spin s gauge theory. The low spin examples are QED3 (s = 1) and the 3-d induced conformal gravity (s = 2). When the original CFT is that of N conformal complex scalar or fermion fields, the U(N) singlet sector of the induced 3-d gauge theory is dual to Vasiliev’s theory in AdS4 with alternate boundary conditions on the spin s massless gauge field. We test this correspondence by calculating the leading term in δF for large N. We show that the coefficient of $ \frac{1}{2} $ log N in δF is equal to the number of spin s − 1 gauge parameters that act trivially on the spin s gauge field. We discuss generalizations of these results to 3-d gauge theories including Chern-Simons terms and to theories where s is half-integer. We also argue that the Weyl anomaly a-coefficients of conformal spin s theories in even dimensions d, such as that of the Weyl-squared gravity in d = 4, can be efficiently calculated using massless spin s fields in AdS d+1 with alternate boundary conditions. Using this method we derive a simple formula for the Weyl anomaly a-coefficients of the d = 4 Fradkin-Tseytlin conformal higher-spin gauge fields. Similarly, using alternate boundary conditions in AdS3 we reproduce the well-known central charge c = −26 of the bc ghosts in 2-d gravity, as well as its higher- spin generalizations.

CMB from CFT

Abstract: During inflation, spacetime is approximately described by de Sitter space which is conformally invariant with the symmetry group SO(1,4). This symmetry can significantly constrain the quantum perturbations which arise in the inflationary epoch. We consider a general situation of single field inflation and show that the three point function involving two scalar modes and one tensor mode is uniquely determined, up to small corrections, by the conformal symmetries. Special conformal transformations play an important role in our analysis. Our result applies only to models where the inflaton sector also approximately preserves the full conformal group and shows that this three point function is a good way to test if special conformal invariance was preserved during inflation.

Localization & Exact Holography

Abstract: We consider the AdS 2 /CFT 1 holographic correspondence near the horizon of big four-dimensional black holes preserving four supersymmetries in toroidally compactified Type-II string theory. The boundary partition function of CFT 1 is given by the known quantum degeneracies of these black holes. The bulk partition function is given by a functional integral over string fields in AdS 2. Using recent results on localization we reduce the infinite-dimensional functional integral to a finite number of ordinary integrals over a space of localizing instantons. Under reasonable assumptions about the relevant terms in the effective action, these integrals can be evaluated exactly to obtain a bulk partition function. It precisely reproduces all terms in the exact Rademacher expansion of the boundary partition function as nontrivial functions of charges except for the Kloosterman sum which can in principle follow from an analysis of phases in the background of orbifolded instantons. Our results can be regarded as a step towards proving ‘exact holography’ in that the bulk and boundary partition functions computed independently agree for finite charges. Since the bulk partition function defines the quantum entropy of the black hole, our results enable the evaluation of perturbative as well as nonperturbative quantum corrections to the Bekenstein-Hawking-Wald entropy of these black holes.

Strongly coupled gauge theories: high and low temperature behavior of non-local observables

Abstract: We explore the high and low temperature behavior of non-local observables in strongly coupled gauge theories that are dual to AdS. We develop a systematic expansion for equal time two-point correlation, spatial Wilson loops and entanglement entropy at finite temperature using the AdS/CFT correspondence, leading to analytic expressions for these observables at high and low temperature limits. This approach enables the identification of the contributions of different regions of the bulk geometry to these gauge theory observables.