Showing papers on "AdS/CFT correspondence published in 2009"
TL;DR: Quasinormal modes are eigenmodes of dissipative systems as discussed by the authors, and they serve as an important tool for determining the near-equilibrium properties of strongly coupled quantum field theories, such as viscosity, conductivity and diffusion constants.
Abstract: Quasinormal modes are eigenmodes of dissipative systems. Perturbations of classical gravitational backgrounds involving black holes or branes naturally lead to quasinormal modes. The analysis and classification of the quasinormal spectra require solving non-Hermitian eigenvalue problems for the associated linear differential equations. Within the recently developed gauge-gravity duality, these modes serve as an important tool for determining the near-equilibrium properties of strongly coupled quantum field theories, in particular their transport coefficients, such as viscosity, conductivity and diffusion constants. In astrophysics, the detection of quasinormal modes in gravitational wave experiments would allow precise measurements of the mass and spin of black holes as well as new tests of general relativity. This review is meant as an introduction to the subject, with a focus on the recent developments in the field.
1,592 citations
TL;DR: In this paper, it is shown that small corrections to the leading order Hawking computation cannot remove the entanglement between the radiation and the hole, and that one cannot explain away the information paradox by invoking AdS/CFT duality.
Abstract: The black hole information paradox is a very poorly understood problem. It is often believed that Hawking's argument is not precisely formulated, and a more careful accounting of naturally occurring quantum corrections will allow the radiation process to become unitary. We show that such is not the case, by proving that small corrections to the leading order Hawking computation cannot remove the entanglement between the radiation and the hole. We formulate Hawking's argument as a 'theorem': assuming 'traditional' physics at the horizon and usual assumptions of locality we will be forced into mixed states or remnants. We also argue that one cannot explain away the problem by invoking AdS/CFT duality. We conclude with recent results on the quantum physics of black holes which show that the interior of black holes have a 'fuzzball' structure. This nontrivial structure of microstates resolves the information paradox and gives a qualitative picture of how classical intuition can break down in black hole physics.
1,024 citations
TL;DR: In this article, four lectures on holography and the AdS/CFT correspondence applied to condensed matter systems were presented, the first lecture introduces the concept of a quantum phase transition and the second lecture discusses linear response theory and Ward identities.
Abstract: Four lectures on holography and the AdS/CFT correspondence applied to condensed matter systems 1 . The first lecture introduces the concept of a quantum phase transition. The second lecture discusses linear response theory and Ward identities. The third lecture presents transport coefficients derived from AdS/CFT that should be applicable in the quantum critical region associated with a quantum phase transition. The fourth lecture builds in the physics of a superconducting or superfluid phase transition to the simple holographic model of the third lecture.
1,006 citations
TL;DR: In this article, the authors review recent progress on the holographic understanding of the entanglement entropy in the anti-de Sitter space/conformal field theory (AdS/CFT) correspondence.
Abstract: In this paper, we review recent progress on the holographic understanding of the entanglement entropy in the anti-de Sitter space/conformal field theory (AdS/CFT) correspondence. In general, the AdS/CFT relates physical observables in strongly coupled quantum many-body systems to certain classical quantities in gravity plus matter theories. In the case of our holographic entanglement entropy, its gravity dual turns out to be purely geometric, i.e. the area of minimal area surfaces in AdS spaces. One interesting application is to study various phase transitions by regarding the entanglement entropy as order parameters. Indeed we will see that our holographic calculations nicely reproduce the confinement/deconfinement transition. Our results can also be applied to understanding the microscopic origins of black hole entropy.
984 citations
TL;DR: In this paper, it was shown that any CFT with a large-N expansion and a large gap has a local bulk dual, and that the conjecture is true in a broad range of CFT's, to first nontrivial order in 1/N-2.
Abstract: The locality of bulk physics at distances below the AdS length scale is one of the remarkable aspects of AdS/CFT duality, and one of the least tested. It requires that the AdS radius be large compared to the Planck length and the string length. In the CFT this implies a large-N expansion and a gap in the spectum of anomalous dimensions. We conjecture that the implication also runs in the other direction, so that any CFT with a large-N expansion and a large gap has a local bulk dual. For an abstract CFT we formulate the consistency conditions, most notably crossing symmetry, and show that the conjecture is true in a broad range of CFT's, to first nontrivial order in 1/N-2: in any CFT with a gap and a large-N expansion, the four-point correlator is generated via the AdS/CFT dictionary from a local bulk interaction. We establish this result by a counting argument on each side, and also investigate various properties of some explicit solutions.
947 citations
01 Jan 2009
TL;DR: In this article, it was shown that at the level of linear response the low-frequency limit of a strongly coupled field theory at finite temperature is determined by the horizon geometry of its gravity dual, i.e., by the "membrane paradigm" fluid of classical black hole mechanics.
Abstract: We show that at the level of linear response the low-frequency limit of a strongly coupled field theory at finite temperature is determined by the horizon geometry of its gravity dual, i.e., by the ‘‘membrane paradigm’’ fluid of classical black hole mechanics. Thus, generic boundary theory transport coefficients can be expressed in terms of geometric quantities evaluated at the horizon. When applied to the stress tensor this gives a simple, general proof of the universality of the shear viscosity in terms of the universality of gravitational couplings, and when applied to a conserved current it gives a new general formula for the conductivity. Away from the low-frequency limit the behavior of the boundary theory fluid is no longer fully captured by the horizon fluid even within the derivative expansion; instead, we find a nontrivial evolution from the horizon to the boundary. We derive flow equations governing this evolution and apply them to the simple examples of charge and momentum diffusion.
588 citations
TL;DR: It is found that the mathematics of string theory is capable of describing fermionic quantum critical states, and the spectral functions of fermions in the field theory are computed.
Abstract: A central problem in quantum condensed matter physics is the critical theory governing the zero-temperature quantum phase transition between strongly renormalized Fermi liquids as found in heavy fermion intermetallics and possibly in high-critical temperature superconductors. We found that the mathematics of string theory is capable of describing such fermionic quantum critical states. Using the anti-de Sitter/conformal field theory correspondence to relate fermionic quantum critical fields to a gravitational problem, we computed the spectral functions of fermions in the field theory. By increasing the fermion density away from the relativistic quantum critical point, a state emerges with all the features of the Fermi liquid.
576 citations
TL;DR: In this paper, the effect of general R 2 corrections to the gravitational action in AdS space on the shear viscosity of the dual gauge theory was studied. But the R 2 terms were determined by the central charges of the CFT.
Abstract: We use the real-time finite-temperature AdS/CFT correspondence to compute the effect of general R 2 corrections to the gravitational action in AdS space on the shear viscosity of the dual gauge theory. The R 2 terms in AdS5 are determined by the central charges of the CFT. We present an example of a four-dimensional gauge theory in which the conjectured lower bound of 1/4π on the viscosity-to-entropy ratio is violated for finite N.
460 citations
TL;DR: In this paper, it was shown that at the level of linear response the low-frequency limit of a strongly coupled field theory at finite temperature is determined by the horizon geometry of its gravity dual, i.e., by the ''membrane paradigm'' fluid of classical black hole mechanics.
Abstract: We show that at the level of linear response the low-frequency limit of a strongly coupled field theory at finite temperature is determined by the horizon geometry of its gravity dual, i.e., by the ``membrane paradigm'' fluid of classical black hole mechanics. Thus, generic boundary theory transport coefficients can be expressed in terms of geometric quantities evaluated at the horizon. When applied to the stress tensor this gives a simple, general proof of the universality of the shear viscosity in terms of the universality of gravitational couplings, and when applied to a conserved current it gives a new general formula for the conductivity. Away from the low-frequency limit the behavior of the boundary theory fluid is no longer fully captured by the horizon fluid even within the derivative expansion; instead, we find a nontrivial evolution from the horizon to the boundary. We derive flow equations governing this evolution and apply them to the simple examples of charge and momentum diffusion.
460 citations
TL;DR: In this article, the authors derived the thermodynamic Bethe ansatz equations which should control the spectrum of the planar AdS5/CFT4 correspondence, and the associated set of universal functional relations (Y-system) satisfied by the exponentials of the TBA pseudoenergies.
Abstract: Moving from the mirror theory Bethe?Yang equations proposed by Arutyunov and Frolov, we derive the thermodynamic Bethe ansatz equations which should control the spectrum of the planar AdS5/CFT4 correspondence. The associated set of universal functional relations (Y-system) satisfied by the exponentials of the TBA pseudoenergies is deduced, confirming the structure inferred by Gromov, Kazakov and Vieira.
459 citations
TL;DR: In this paper, the authors discuss recent developments in the hydrodynamic description of strongly coupled conformal field theories using the AdS/CFT correspondence, which provides a map between a class of inhomogeneous, dynamical, black hole solutions in asymptotically AdS spacetimes and arbitrary fluid flows in strongly interacting boundary field theory.
Abstract: We discuss recent developments in the hydrodynamic description of strongly coupled conformal field theories using the AdS/CFT correspondence. In particular, we review aspects of the fluid-gravity correspondence which provides a map between a class of inhomogeneous, dynamical, black hole solutions in asymptotically AdS spacetimes and arbitrary fluid flows in the strongly interacting boundary field theory. We explain how the geometric duals to the fluid dynamics are constructed in a boundary derivative expansion and use the construction to extract the hydrodynamic transport coefficients. In addition, we also describe the recent developments extending the correspondence to incorporate matter fields and to non-relativistic systems. Based on lectures given at the CERN Winter School on Supergravity, Strings and Gauge Theories, Geneva, Switzerland (February 2009).
TL;DR: Using seven-dimensional Sasaki-Einstein spaces, this work constructs solutions of D=11 supergravity that are holographically dual to superconductors in three spacetime dimensions and indicates a new zero temperature solution dual to a quantum critical point.
Abstract: Using seven-dimensional Sasaki-Einstein spaces we construct solutions of D=11 supergravity that are holographically dual to superconductors in three spacetime dimensions. Our numerical results indicate a new zero temperature solution dual to a quantum critical point.
TL;DR: In this article, a review of the current understanding of strongly coupled quark-gluon plasma (sQGP) is presented, especially theoretical progress in explaining the RHIC data by hydrodynamics, describing lattice data using electric-magnetic duality; and understanding of gauge-string duality known as AdS/CFT and its application for ''conformal" plasma.
TL;DR: In this article, the string dual of the recently constructed N=6 superconformal Chern-Simons theory of Aharony, Bergman, Jafferis and Maldacena (ABJM theory) was examined in particular on the SU(2)×SU(2)-sector.
TL;DR: The existence and uniqueness of black-hole solutions of 5D dilaton gravity with a monotonic dilaton potential were analyzed in detail in detail as discussed by the authors, and it was shown that such theories are holographically very close to pure Yang-Mills theory in four dimensions.
Abstract: The asymptotically-logarithmically-AdS black-hole solutions of 5D dilaton gravity with a monotonic dilaton potential are analyzed in detail. Such theories are holographically very close to pure Yang-Mills theory in four dimensions. The existence and uniqueness of black-hole solutions is shown. It is also shown that a Hawking-Page transition exists at finite temperature if and only if the potential corresponds to a confining theory. The physics of the transition matches in detail with that of deconfinement of the Yang-Mills theory. The high-temperature phase asymptotes to a free gluon gas at high temperature matching the expected behavior from asymptotic freedom. The thermal gluon condensate is calculated and shown to be crucial for the existence of a non-trivial deconfining transition. The condensate of the topological charge is shown to vanish in the deconfined phase.
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TL;DR: In this paper, the Kovtun-Son-Starinets viscosity bound is violated in superconformal gauge theories with non-equal central charges c≠a.
Abstract: We use a low-energy effective description of gauge theory/string theory duality to argue that the Kovtun-Son-Starinets viscosity bound is generically violated in superconformal gauge theories with non-equal central charges c≠a. We present new examples (of string theory constructions and of gauge theories) where the bound is violated in a controllable setting. We consider the comparison of results from AdS/CFT calculations to the QCD plasma in the context of this discussion.
TL;DR: In this paper, a simple derivation of the real-time AdS/CFT prescription is discussed as an analytic continuation of the corresponding problem in Euclidean signature, and the formalism is extended to spinor operators.
Abstract: We discuss a simple derivation of the real-time AdS/CFT prescription as an analytic continuation of the corresponding problem in Euclidean signature. We then extend the formalism to spinor operators and apply it to the examples of real-time fermionic correlators in CFTs dual to pure AdS and the BTZ black hole.
TL;DR: In this paper, a model of 3+1 dimensional gravity with negative cosmological constant coupled to abelian gauge fields has been proposed as a gravity dual for Lifshitz like critical phenomena in 2+1 dimensions.
Abstract: A model of 3+1 dimensional gravity with negative cosmological constant coupled to abelian gauge fields has been proposed as a gravity dual for Lifshitz like critical phenomena in 2+1 dimensions. The finite temperature behavior is described by black holes that are asymptotic to the Lifshitz fixed point geometry. There is a one-parameter family of charged black holes, where the magnitude of the charge is uniquely determined by the black hole area. These black holes are thermodynamically stable and become extremal in the limit of vanishing size. The theory also has a discrete spectrum of localized objects described by non-singular spacetime geometries. The finite temperature behavior of Wilson loops is reminiscent of strongly coupled gauge theories in 3+1 dimensions, including screening at large distances.
TL;DR: In this paper, the stability of a landscape of IR fixed points of large N gauge theories in 2+1 dimensions was studied and it was shown that many of these theories have charged operators that condense when the theory is placed at a finite chemical potential.
Abstract: The AdS/CFT correspondence may connect the landscape of string vacua and the 'atomic landscape' of condensed matter physics. We study the stability of a landscape of IR fixed points of N=2 large N gauge theories in 2+1 dimensions, dual to Sasaki-Einstein compactifications of M theory, toward a superconducting state. By exhibiting instabilities of charged black holes in these compactifications, we show that many of these theories have charged operators that condense when the theory is placed at a finite chemical potential. We compute a statistical distribution of critical superconducting temperatures for a subset of these theories. With a chemical potential of 1 mV, we find critical temperatures ranging between 0.24 and 165 K.
TL;DR: In this article, the authors use the AdS/CFT correspondence to study the thermalization of a strongly coupled conformal field theory that is forced out of its vacuum by a source that couples to a marginal operator.
Abstract: We use the AdS/CFT correspondence to study the thermalization of a strongly coupled conformal field theory that is forced out of its vacuum by a source that couples to a marginal operator. The source is taken to be of small amplitude and finite duration, but is otherwise an arbitrary function of time. When the field theory lives on $R^{d-1,1}$, the source sets up a translationally invariant wave in the dual gravitational description. This wave propagates radially inwards in $AdS_{d+1}$ space and collapses to form a black brane. Outside its horizon the bulk spacetime for this collapse process may systematically be constructed in an expansion in the amplitude of the source function, and takes the Vaidya form at leading order in the source amplitude. This solution is dual to a remarkably rapid and intriguingly scale dependent thermalization process in the field theory. When the field theory lives on a sphere the resultant wave either slowly scatters into a thermal gas (dual to a glueball type phase in the boundary theory) or rapidly collapses into a black hole (dual to a plasma type phase in the field theory) depending on the time scale and amplitude of the source function. The transition between these two behaviors is sharp and can be tuned to the Choptuik scaling solution in $R^{d,1}$.
TL;DR: In this article, it was shown that three-dimensional massive gravity admits Lifshitz metrics with generic values of the dynamical exponent $z$ as exact solutions at the point $z = 3.
Abstract: We show that three-dimensional massive gravity admits Lifshitz metrics with generic values of the dynamical exponent $z$ as exact solutions. At the point $z=3$, exact black hole solutions that are asymptotically Lifshitz arise. These spacetimes are three-dimensional analogues of those that were recently proposed as gravity duals for anisotropic scale invariant fixed points.
TL;DR: In this article, a relation between extremal black hole entropy and degeneracy of micro states using AdS2/CFT1 correspondence was found. But the relation between entropy and microstate degeneracy was not defined.
Abstract: We review and extend recent attempts to find a precise relation between extremal black hole entropy and degeneracy of microstates using AdS2/CFT1 correspondence. Our analysis leads to a specific relation between degeneracy of black hole microstates and an appropriately defined partition function of string theory on the near horizon geometry — named the quantum entropy function. In the classical limit this reduces to the usual relation between statistical entropy and Wald entropy.
TL;DR: In this article, the authors consider the thermal and hydrodynamic properties of the plasma in the dual CFT and calculate the ratio of shear viscosity to entropy density and argue that the violation of the KSS bound is enhanced in the presence of a chemical potential.
Abstract: We consider five-dimensional gravity coupled to a negative cosmological constant and a single U(1) gauge field, including a general set of four-derivative interactions. In this framework, we construct charged planar AdS black hole solutions perturbatively and consider the thermal and hydrodynamic properties of the plasma in the dual CFT. In particular, we calculate the ratio of shear viscosity to entropy density and argue that the violation of the KSS bound is enhanced in the presence of a chemical potential. We also compute the electrical conductivity and comment on various conjectured bounds related to this coefficient.
TL;DR: In this article, it was shown that the microscopic entropy and the Bekenstein-Hawking entropy of the extremal Kerr-AdS metric agree also for four dimensions, and also for extremal four-dimensional Kerr metrics in dimensions 5, 6 and 7.
Abstract: It was proposed recently that the near-horizon states of an extremal four-dimensional Kerr black hole could be identified with a certain chiral conformal field theory whose Virasoro algebra arises as an asymptotic symmetry algebra of the near-horizon Kerr geometry. Supportive evidence for the proposed duality came from the equality of the microscopic entropy of the CFT, calculated by means of the Cardy formula, and the Bekenstein-Hawking entropy of the extremal Kerr black hole. In this paper we examine the proposed Kerr/CFT correspondence in a broader context. In particular, we show that the microscopic entropy and the Bekenstein-Hawking entropy agree also for the extremal Kerr-AdS metric in four dimensions, and also for the extremal Kerr-AdS metrics in dimensions 5, 6 and 7. General formulae for all higher dimensions are also presented.
TL;DR: In this paper, the authors present type IIB supergravity solutions which are expected to be dual to certain Lifshitz-like fixed points with anisotropic scale invariance.
Abstract: We present type IIB supergravity solutions which are expected to be dual to certain Lifshitz-like fixed points with anisotropic scale invariance. They are expected to describe a class of D3-D7 systems and their finite temperature generalizations are straightforward. We show that there exist solutions that interpolate between these anisotropic solutions in the IR and the standard AdS5 solutions in the UV. This predicts anisotropic RG flows from familiar isotropic fixed points to anisotropic ones. In our case, these RG flows are triggered by a non-zero theta-angle in Yang-Mills theories that linearly depends on one of the spatial coordinates. We study the perturbations around these backgrounds and discuss the possibility of instability. We also holographically compute their thermal entropies, viscosities, and entanglement entropies.
TL;DR: In this article, three holographic constructions of fractional quantum Hall effect (FQHE) via string theory are presented, using supersymmetric domain walls in = 6 Chern-Simons theory.
Abstract: We present three holographic constructions of fractional quantum Hall effect (FQHE) via string theory. The first model studies edge states in FQHE using supersymmetric domain walls in = 6 Chern-Simons theory. We show that D4-branes wrapped on 1 or D8-branes wrapped on 3 create edge states that shift the rank or the level of the gauge group, respectively. These holographic edge states correctly reproduce the Hall conductivity. The second model presents a holographic dual to the pure U(N)k (Yang-Mills-)Chern-Simons theory based on a D3-D7 system. Its holography is equivalent to the level-rank duality, which enables us to compute the Hall conductivity and the topological entanglement entropy. The third model introduces the first string theory embedding of hierarchical FQHEs, using IIA string on 2/Zn.
TL;DR: In this paper, a class of black hole solutions to a (3+1) dimensional theory coupled to abelian gauge fields with negative cosmological constant was proposed as the dual theory to a Lifshitz theory describing critical phenomena in 2+1 dimensions.
Abstract: I find a class of black hole solutions to a (3+1) dimensional theory gravity coupled to abelian gauge fields with negative cosmological constant that has been proposed as the dual theory to a Lifshitz theory describing critical phenomena in (2+1) dimensions. These black holes are all asymptotic to a Lifshitz fixed point geometry and depend on a single parameter that determines both their area (or size) and their charge. Most of the solutions are obtained numerically, but an exact solution is also obtained for a particular value of this parameter. The thermodynamic behaviour of large black holes is almost the same regardless of genus, but differs considerably for small black holes. Screening behaviour is exhibited in the dual theory for any genus, but the critical length at which it sets in is genus-dependent for small black holes.
TL;DR: In this paper, the authors studied a supercurrent solution and the associated phase diagram and found a critical point in the phase diagram where the second order superconducting phase transition becomes first order.
Abstract: Hartnoll, Herzog, and Horowitz [Phys. Rev. Lett. 101, 031601 (2008).] discuss a holographic black hole solution which exhibits a superconductorlike transition. In the superconducting phase the black holes show infinite DC conductivity. This gives rise to the possibility of deforming the solutions by turning on a time independent current (supercurrent), without any electric field. This type of deformation does not exist for normal (nonsuperconducting) black holes, due to the no-hair theorems. In this paper we have studied such a supercurrent solution and the associated phase diagram. Interestingly, we have found a 'special point' (critical point) in the phase diagram where the second order superconducting phase transition becomes first order. Supercurrent in superconducting materials is a well studied phenomenon in condensed matter systems. We have found some qualitative agreement with known results.
TL;DR: In this article, the poles of the retarded Green functions of a holographic superconductor were studied and the spectrum of quasinormal frequencies in the broken phase, where the appearance of a massless or hydrodynamic mode at the critical temperature was established.
Abstract: We study the poles of the retarded Green functions of a holographic superconductor. The model shows a second order phase transition where a charged scalar operator condenses and a U(1) symmetry is spontaneously broken. The poles of the holographic Green functions are the quasinormal modes in an AdS black hole background. We study the spectrum of quasinormal frequencies in the broken phase, where we establish the appearance of a massless or hydrodynamic mode at the critical temperature as expected for a second order phase transition. In the broken phase we find the pole representing second sound. We compute the speed of second sound and its attenuation length as function of the temperature. In addition we find a pseudo diffusion mode, whose frequencies are purely imaginary but with a non-zero gap at zero momentum. This gap goes to zero at the critical temperature. As a technical side result we explain how to calculate holographic Green functions and their quasinormal modes for a set of operators that mix under the RG flow.
TL;DR: In this paper, the authors calculate the shear viscosity of field theories with gravity duals of Gauss-Bonnet gravity with a nontrivial dilaton using anti-de Sitter/conformal field theory.
Abstract: We calculate the shear viscosity of field theories with gravity duals of Gauss-Bonnet gravity with a nontrivial dilaton using anti-de Sitter/conformal field theory. We find that the dilaton field has a nontrivial contribution to the ratio of shear viscosity over entropy density, and, after imposing a causal constraint for the boundary field theory, the new lower bound 4/25 pi, obtained from pure Gauss-Bonnet gravity, may have a small violation.