Holographic probes of anti-de Sitter spacetimes

Nuclear Physics B, 2001

We analyse the Seiberg Witten curve describing the N = 2 gauge theory dual to the supergravity solution with fractional branes. Emphasis is given to those aspects that are related to stringy mechanism known as the enhançon. We also compare our results with the features of the supergravity duals, which have been variously interpreted in the literature. Known aspects of the N = 2 gauge theories seem to agree with the supergravity solution, whenever the two theories can be faithfully compared.

Physical Review D, 2005

Field theory in de Sitter space admits a one-parameter family of vacua determined by a superselection parameter alpha. Of these vacua, the Euclidean vacuum uniquely extrapolates to the vacuum of flat Minkowski space. States which resemble the alpha-vacua can be constructed as excitations above the Euclidean vacuum. Such states have modes alpha(k) which decay faster that k(1-d)/2. Fields in such

Physical Review D, 2001

Exploring the role of conformal theories of gravity in string theory, we show that the minimal (N=2) gauged supergravities in five dimensions induce the multiplets and transformations of N=1 four-dimensional conformal supergravity on the spacetime boundary. N=1 Poincaré supergravity can be induced by explicitly breaking the conformal invariance via a radial cutoff in the 5D space. The AdS/CFT correspondence relates

Physical Review D, 2001

A uniformly acclerated observer in anti-deSitter spacetime is known to detect thermal radiation when the acceleration exceeds a critical value. We investigate the holographic interpretation of this phenomenon. For uniformly accelerated trajectories transverse to the boundary of the AdS space, the hologram is a blob which expands along the boundary. Observers on the boundary co-moving with the hologram become observers in cosmological spacetimes. For supercritical accelerations one gets a Milne universe when the holographic screen is the boundary in Poincaré coordinates, while for the boundary in hyperspherical coordinates one gets deSitter spacetimes. The presence or absence of thermality is then interpreted in terms of specific classes of observers in these cosmologies.

Journal of High Energy Physics, 2002

We study aspects of the propagation of strings on BTZ black holes. After performing a careful analysis of the global spacetime structure of generic BTZ black holes, and its relation to the geometry of the SL(2, R) group manifold, we focus on the simplest case of the massless BTZ black hole. We study the SL(2, R) Wess-Zumino-Witten model in the worldsheet minisuperspace limit, taking into account special features associated to the Lorentzian signature of spacetime. We analyse the two-and three-point functions in the pointparticle limit. To lay bare the underlying group structure of the correlation functions, we derive new results on Clebsch-Gordan coefficients for SL(2, R) in a parabolic basis. We comment on the application of our results to string theory in singular time-dependent orbifolds, and to a Lorentzian version of the AdS/CF T correspondence.

Journal of High Energy Physics, 2003

We clarify aspects of the holographic AdS/CFT correspondence that are typical of Lorentzian signature, to lay the foundation for a treatment of time-dependent gravity and conformal field theory phenomena. We provide a derivation of bulk-to-boundary propagators associated to advanced, retarded and Feynman bulk propagators, and provide a better understanding of the boundary conditions satisfied by the bulk fields at the horizon. We interpret the subleading behavior of the wavefunctions in terms of specific vacuum expectation values, and compute two-point functions in our framework. We connect our bulk methods to the closed time path formalism in the boundary field theory.

Physical Review D, 2004

We construct the exact solution of one (anti)instanton in N = 1 2 super Yang-Mills theory defined on non(anti)commutative superspace. We first identify N = 1 2 superconformal invariance as maximal spacetime symmetry. For gauge group U(2), the SU(2) part of the solution is given by the standard (anti)instanton, but the U(1) field strength also turns out nonzero. The solution is SO(4) rotationally symmetric. For gauge group U(N), in contrast to the U(2) case, we show that the entire U(N) part of the solution is deformed by non(anti)commutativity and fermion zero-modes. The solution is no longer rotationally symmetric; it is polarized into an axially symmetric configuration because of the underlying non(anti)commutativity. We compute the 'information metric' of one (anti)instanton. We find that the moduli space geometry is deformed from hyperbolic space H 5 (Euclidean anti-de Sitter space) in a way anticipated from reduced spacetime symmetry. Remarkably, the volume measure of the moduli space turns out to be independent of the non(anti)commutativity. Implications for D-branes in Ramond-Ramond flux background and the gauge-gravity correspondence are discussed.

International Journal of Modern Physics A, 2009

Physical Review Letters, 2009

We derive the equations of cosmological evolution from an AdS Schwarzschild black hole via holographic renormalization with appropriate boundary conditions.

Classical and Quantum Gravity, 2013

We consider general black hole solutions in five-dimensional spacetime in the presence of a negative cosmological constant. We obtain a cosmological evolution via the gravity/gauge theory duality (holography) by defining appropriate boundary conditions on a four-dimensional boundary hypersurface. The standard counterterms are shown to renormalize the bare parameters of the system (the four-dimensional Newton's constant and cosmological constant). We discuss the thermodynamics of cosmological evolution and present various examples. The standard braneworld scenarios are shown to be special cases of our holographic construction. †

Physical Review D, 2016

In the AdS/CFT correspondence, CFTs are identified by asymptotic boundary surfaces and the boundary conditions imposed on those surfaces. However, AdS can be foliated in various ways to give different boundaries. We show that the CFTs obtained using certain distinct foliations are different. This difference arises because the asymptotic region of a foliation overlaps with the deep interior region of another. In particular we focus on the CFTs defined on surfaces of large constant radius in global coordinates, Rindler-AdS coordinates, and Poincaré coordinates for AdS 3 . We refer to these as global-CFT, Rindler-CFT and Poincaré-CFT respectively. We demonstrate that the correlators for these CFTs are different and argue that the bulk duals to these should agree up to very close to the respective horizons but then start differing. Since the BTZ black hole is obtained as a quotient of AdS 3 , we discuss the implications of our results for bulk duals of periodically-identified Poincaré and Rindler-CFTs. Our results are consistent with some recent proposals suggesting a modification of the semi-classical BTZ geometry close to the horizons.

Physical Review D, 2015

We construct two interpolating solutions in type II string theory which interpolate between an AdS 5 in the UV and a hyperscaling violating three (spatial) dimensional Lifshitz space-time in the IR. The first solution is non-supersymmetric and is obtained from a known intersecting non-supersymmetric D3-brane with chargeless D0-brane solution of type IIB string theory, by restricting some parameters characterizing the solution and going to a new coordinate. In the IR the dilaton is non-constant in general and the metric is three (spatial) dimensional hyperscaling violating Lifshitz with dynamical critical exponent z = (3 + 3γ)/(3 − γ) and hyperscaling violation exponent θ = 12/(3 − γ), where γ is a real parameter and can take continuous values from −1 to +1. At the two extreme values, i.e., for γ = ±1, the dilaton is constant. On physical grounds it is found that γ must be restricted to lie in the range −1 ≤ γ ≤ 0. The second solution is supersymmetric and is obtained from the known F-D2 bound state solution of type IIA string theory by zooming into a particular region of space. In the UV, the proper description is given in a T-dual frame which is AdS 5 , whereas in the IR, it gives a three dimensional hyperscaling violating Lifshitz with z = 3 and θ = 2 = d − 1.

Fortschritte der Physik, 2013

General relativity contains solutions in which two distant black holes are connected through the interior via a wormhole, or Einstein-Rosen bridge. These solutions can be interpreted as maximally entangled states of two black holes that form a complex EPR pair. We suggest that similar bridges might be present for more general entangled states. In the case of entangled black holes one can formulate versions of the AMPS(S) paradoxes and resolve them. This suggests possible resolutions of the firewall paradoxes for more general situations.

Physical Review Letters, 2002

For n+1 dimensional asymptotically AdS spacetimes which have holographic duals on their n dimensional conformal boundaries, we show that the imposition of causality on the boundary theory is sufficient to prove positivity of mass for the spacetime when n ≥ 3, without the assumption of any local energy condition. We make crucial use of a generalization of the time-delay formula calculated in gr-qc/9404019, which relates the time delay of a bulk null curve with respect to a boundary null geodesic to the Ashtekar-Magnon mass of the spacetime. We also discuss holographic causality for the negative mass AdS soliton and its implications for the positive energy conjecture of Horowitz and Myers.

Physical Review D, 2000

We study SU (N) → S(U (N/2) × U (N/2)) symmetry breaking in N = 4 SY M via AdS/CFT correspondence. Two stacks of N 2 parallel D3 branes are separated by a distance 2d in the transverse directions. This leads to an interaction between different l-wave dilatonic KK modes when expanded in S 5 harmonics. We calculate certain two point correlation functions of the dual gauge theory in the decoupling limit d α ′ ≪ 1. Due to mode mixing, the diagonal correlation functions have 1 N conformal-like correction as well as deformation terms. The off-diagonal correlators are also nonvanishing and their leading order is 1 N. We discuss briefly the spectrum of the glueball exitations.

Journal of High Energy Physics, 2006

We study the AdS/CFT correspondence as a probe of inflation. We assume the existence of a string landscape containing at least one stable AdS vacuum and a (nearby) metastable de Sitter state. Standard arguments imply that the bulk physics in the vicinity of the AdS minimum is described by a boundary CFT. We argue that large enough bubbles of the dS phase, including those able to inflate, are described by mixed states in the CFT. Inflating degrees of freedom are traced over and do not appear explicitly in the boundary description. They nevertheless leave a distinct imprint on the mixed state. In the supergravity approximation, analytic continuation connects AdS/CFT correlators to dS/CFT correlators. This provides a framework for extracting further information as well. Our work also shows that no scattering process can create an inflating region, even by quantum tunneling, since a pure state can never evolve into a mixed state under unitary evolution.

Classical and Quantum Gravity, 2010

To study thermal aspects of the ABJM theory in the strongly coupled regime, we carry out the CP 3 invariant dimensional reduction of the type IIA supergravity down to four dimensions. We then investigate zero and finite temperature responses of the operators which are dual to the AdS scalar and vector fields. Two scalar operators are shown to have finite-temperature condensations by coupling of constant source term. The currents dual to the massless and massive gauge fields are not induced by coupling of constant boundary vector potential, which implies that the phase described by black brane background is not superconducting. We also discuss a generalization to charged (dyonic) black holes.

Journal of High Energy Physics, 2018

We present a spherically symmetric aAdS gravity solution with Schwinger-Keldysh boundary condition dual to a CFT at finite temperature defined on a complex time contour. The geometry is built by gluing the exterior of a two-sided AdS Black Hole, the (aAdS) Einstein-Rosen wormhole, with two Euclidean black hole halves. These pieces are interpreted as the gravity duals of the two Euclidean β/2 segments in the SK path, each coinciding with a Hartle-Hawking-Maldacena (TFD) vacuum state, while the Lorentzian regions naturally describes the real-time evolution of the TFD doubled system. Within the context of Skenderis and van Rees real-time holographic prescription, the new solution should be compared to the Thermal AdS spacetime since both contribute to the gravitational path integral. In this framework, we compute the time ordered 2-pt functions of scalar CFT operators via a non-back-reacting Klein-Gordon field for both backgrounds and confront the results. When solving for the field we...

Physical Review D, 2000

The general correlator of composite operators of N=4 supersymmetric gauge field theory is divergent. We introduce a means for renormalizing these correlators by adding a boundary theory on the AdS space correcting for the divergences. Such renormalizations are not equivalent to the standard normal ordering of current algebras in two dimensions. The correlators contain contact terms that contribute to the OPE; we relate them diagrammatically to correlation functions of compound composite operators dual to multi-particle states.

Physical Review D, 2016

We consider a time-dependent deformation of anti-de-Sitter (AdS) space-time which contains a spacelike "singularity"-a space-like region of high curvature. Making use of the AdS/CFT correspondence we can map the bulk dynamics onto the boundary. The boundary theory has a time dependent coupling constant which becomes small at times when the bulk space-time is highly curved. We investigate the propagation of small fluctuations of a test scalar field from early times before the bulk singularity to late times after the singularity. Under the assumption that the AdS/CFT correspondence extends to deformed AdS space-times, we can map the bulk evolution of the scalar field onto the evolution of the boundary gauge field. The time evolution of linearized fluctuations is well defined in the boundary theory as long as the coupling remains finite, so that we can extend the boundary perturbations to late times after the singularity. Assuming that the spacetime in the future of the singularity has a weakly coupled region near the boundary, we reconstruct the bulk fluctuations after the singularity crossing making use of generic properties of boundary-to-bulk propagators. Finally, we extract the spectrum of the fluctuations at late times given some initial spectrum. We find that the spectral index is unchanged, but the amplitude increases due to the squeezing of the fluctuations during the course of the evolution. This investigation can teach us important lessons on how the spectrum of cosmological perturbations passes through a bounce which is singular from the bulk point of view but which is resolved using an ultraviolet complete theory of quantum gravity.

Physical Review D, 1999

We discuss various approaches to extracting the full stress-energy tensor of the conformal field theory from the corresponding supergravity solutions, within the framework of the Maldacena conjecture. This provides a more refined probe of the AdS/CFT correspondence. We apply these techniques in considering the Casimir energy of the conformal field theory on a torus. It seems that either generically the corresponding supergravity solutions are singular (i.e., involve regions of large string-scale curvatures), or that they are largely insensitive to the boundary conditions of the CFT on the torus.

Physical Review D, 2004

We give an explicit formulation of the time dependent AdS/CFT correspondence when there are multiple vacua present in Lorentzian signature. By computing sample two point functions we show how different amplitudes are related by cosmological particle production. We illustrate our methods in two example spacetimes: (a) a "bubble of nothing" in AdS space, and (b) an asymptotically locally AdS spacetime with a bubble of nothing on the boundary. In both cases the α-vacua of de Sitter space make an interesting appearance.

Physical Review D, 2012

We present a dimensionally deconstructed model of an s-wave holographic superconductor. The 2+1 dimensional model includes multiple charged Cooper pair fields and neutral exciton fields that have interactions governed by hidden local symmetries. We derive AdS/CFT-like relations for the current and charge density in the model, and we analyze properties of the Cooper pair condensates and the complex conductivity.

Physical Review D, 2006

We rederive AdS/CFT predictions for infrared two-point functions by an entirely four dimensional approach, without reference to holography. This approach, originally due to Migdal in the context of QCD, utilizes an extrapolation from the ultraviolet to the infrared using a Padé approximation of the two-point function. We show that the Padé approximation and AdS/CFT give the same leading order predictions, and we discuss including power corrections such as those due to condensates of gluons and quarks in QCD. At finite order the Padé approximation provides a gauge invariant regularization of a higher dimensional gauge theory in the spirit of deconstructed extra dimensions. The radial direction of anti-de Sitter space emerges naturally in this approach.

Physical Review D, 2009

Estimates of the light hadron masses, decay constants and couplings in AdS/QCD models are generally more accurate than should have been expected. Certain predictions based on the AdS/CFT correspondence, such as the ratio of the equilibrium viscosity to entropy density, are universal and therefore provide firm experimental tests of these models. Other observables, while not completely universal, may be relatively insensitive to model details. We calculate the dependence of a number of low-energy hadronic observables on details of the hard-wall AdS/QCD model. In particular, we vary the infrared boundary conditions, the 5D gauge coupling, and the mass of the field responsible for chiral symmetry breaking, while holding fixed a small number of observables. We also find a generalized Gell-Mann-Oakes-Renner relation which helps to justify the identification of model parameters with the product of physical quark mass and chiral condensate as per the AdS/CFT correspondence.

Physical Review D, 1999

We examine the recently proposed technique of adding boundary counterterms to the gravitational action for spacetimes which are locally asymptotic to anti-de Sitter spacetimes. In particular, we explicitly identify higher order counterterms, which allow us to consider spacetimes of dimensions dр7. As the counterterms eliminate the need of ''background subtraction'' in calculating the action, we apply this technique to study examples where the appropriate background was ambiguous or unknown: topological black holes, Taub-NUT-AdS and Taub-Bolt-AdS. We also identify certain cases where the covariant counterterms fail to render the action finite, and we comment on the dual field theory interpretation of this result. In some examples, the case of a vanishing cosmological constant may be recovered in a limit, which allows us to check results and resolve ambiguities in certain asymptotically flat spacetime computations in the literature. ͓S0556-2821͑99͒07318-X͔

Physical review, 2016

Motivated by the task of understanding microscopic dynamics of an evolving black hole, we present a scheme describing gauge-fixed continuous time evolution of quantum gravitational processes in asymptotically flat spacetime using the algebra of CFT operators. This allows us to study the microscopic dynamics of the Hawking emission process, although obtaining a full S-matrix may require a modification of the minimal scheme. The role of the operator product expansion is to physically interpret the resulting time evolution by decomposing the Hilbert space of the states for the entire system into those for smaller subsystems. We translate the picture of an evaporating black hole previously proposed by the authors into predictions for nonperturbative properties of the CFTs that have weakly coupled dual gravitational descriptions. We also discuss a possible relationship between the present scheme and a reference frame change in the bulk.

Physical review, 2010

We use a WKB approximation to establish a relation between the wavefront velocity in a strongly coupled theory and the local speed of light in a holographic dual, with our main focus put on systems with Lifshitz scaling with dynamical exponent z. We then use Einstein equations to relate the behavior of the local speed of light in the bulk with the null energy condition (NEC) for bulk matter, and we show that it is violated for Lifshitz backgrounds with z < 1. We study signal propagation in the gravity dual and show that violations of the NEC are incompatible with causality in the strongly coupled theory, ruling out as holographic models Lifshitz backgrounds with z < 1. We argue that causality violations in z < 1 theories will show up in correlators as superluminal modes and confirm this for a particular example with z = 1/2. Finally, as an application, we use z < 1 solutions to uncover regions of the parameter space of curvature squared corrections to gravity where the NEC can be violated.

Journal of High Energy Physics, 2021

We holographically study the finite-size scaling effects on macroscopic and microscopic quantum correlations deformed by excitation and condensation. The excitation (condensation) increases (decreases) the entanglement entropy of the system. We also investigate the two-point correlation function of local operators by calculating the geodesic length connecting two local operators. As opposed to the entanglement entropy case, the excitation (condensation) decreases (increases) the two-point function. This is because the screening effect becomes strong in the background with the large entanglement entropy. We further show that the holographic renormalization leads to the qualitatively same two-point function as the one obtained from the geodesic length.

Journal of High Energy Physics, 2003

We demonstrate how to compute real-time Green's functions for a class of finite temperature field theories from their AdS gravity duals. In particular, we reproduce the 2 × 2 Schwinger-Keldysh matrix propagator from a gravity calculation. Our methods should work also for computing higher point Lorentzian signature correlators. We elucidate the boundary condition subtleties which hampered previous efforts to build a Lorentzian-signature AdS/CFT correspondence. For two-point correlators, our construction is automatically equivalent to the previously formulated prescription for the retarded propagator.

Journal of High Energy Physics, 2002

We formulate a prescription for computing Minkowski-space correlators from AdS/CFT correspondence. This prescription is shown to give the correct retarded propagators at zero temperature in four dimensions, as well as at finite temperature in the two-dimensional conformal field theory dual to the BTZ black hole. Using the prescription, we calculate the Chern-Simons diffusion constant of the finite-temperature N = 4 supersymmetric Yang-Mills theory in the strong coupling limit. We explain why the quasinormal frequencies of the asymptotically AdS background correspond to the poles of the retarded Green's function of the boundary conformal field theory.