arXiv subjects

Sergey N. Solodukhin

Publications and source records attributed to Sergey N. Solodukhin.

At least 55 records · Page 3Linked to original sources

arXiv2010

Entanglement entropy of round spheres

We propose that the logarithmic term in the entanglement entropy computed in a conformal field theory for a $(d-2)$-dimensional round sphere in Minkowski spacetime is identical to the logarithmic term in the entanglement entropy of extreme black hole. The near-horizon geometry of the latter is $H_2\times S_{d-2}$. For a scalar field this proposal is checked by direct calculation. We comment on relation of this and earlier calculations to the ``brick wall'' model of 't Hooft. The case of generic 4d conformal field theory is discussed.

hep-th↗

arXiv2010

Gravitational effective action and entanglement entropy in UV modified theories with and without Lorentz symmetry

We calculate parameters in the low energy gravitational effective action and the entanglement entropy in a wide class of theories characterized by improved ultraviolet (UV) behavior. These include i) local and non-local Lorentz invariant theories in which inverse propagator is modified by higher-derivative terms and ii) theories described by non-Lorentz invariant Lifshitz type field operators. We demonstrate that the induced cosmological constant, gravitational couplings and the entropy are sensitive to the way the theory is modified in UV. For non-Lorentz invariant theories the induced gravitational effective action is of the Horava-Lifshitz type. We show that under certain conditions imposed on the dimension of the Lifshitz operator the couplings of the extrinsic curvature terms in the effective action are UV finite. Throughout the paper we systematically exploit the heat kernel method appropriately generalized for the class of theories under consideration.

hep-th↗

arXiv2010

Short-distance regularity of Green's function and UV divergences in entanglement entropy

Reformulating our recent result (arXiv:1007.1246 [hep-th]) in coordinate space we point out that no matter how regular is short-distance behavior of Green's function the entanglement entropy in the corresponding quantum field theory is always UV divergent. In particular, we discuss a recent example by Padmanabhan (arXiv:1007.5066 [gr-qc]) of a regular Green's function and show that provided this function arises in a field theory the entanglement entropy in this theory is UV divergent and calculate the leading divergent term.

hep-th↗

arXiv2010

Entanglement Entropy in Non-Relativistic Field Theories

We calculate entanglement entropy in a non-relativistic field theory described by the Schrödinger operator. We demonstrate that the entropy is characterized by i) the area law and ii) UV divergences that are identical to those in the relativistic field theory. These observations are further supported by a holographic consideration. We use the non-relativistic symmetry and completely specify entanglement entropy in large class of non-relativistic theories described by the field operators polynomial in derivatives. We suggest that the area law of the entropy can be tested in experiments with condensed matter systems such as liquid helium.

hep-th↗

arXiv2009

The volume of causal diamonds, asymptotically de Sitter space-times and irreversibility

In this note we prove that the volume of a causal diamond associated with an inertial observer in asymptotically de Sitter 4-dimensional space-time is monotonically increasing function of cosmological time. The asymptotic value of the volume is that of in maximally symmetric de Sitter space-time. The monotonic property of the volume is checked in two cases: in vacuum and in the presence of a massless scalar field. In vacuum, the volume flow (with respect to cosmological time) asymptotically vanishes if and only if future space-like infinity is 3-manifold of constant curvature. The volume flow thus represents irreversibility of asymptotic evolution in spacetimes with positive cosmological constant.

hep-th↗

arXiv2008

Quasi-Normal Modes in Topologically Massive Gravity

We determine the black hole quasi-normal mode spectrum for tensor perturbations in topologically massive AdS-gravity. In the special case of chiral gravity quasi-normal modes are absent despite of the presence of a horizon. In the process we uncover a simple algebraic structure in the quasi normal modes spectrum: the tower of QNM's consists of descendents of a "chiral highest weight'' QNM which in turn satisfies a first order equation.

hep-th↗

arXiv2008

Entanglement entropy, conformal invariance and extrinsic geometry

We use the conformal invariance and the holographic correspondence to fully specify the dependence of entanglement entropy on the extrinsic geometry of the 2d surface $Σ$ that separates two subsystems of quantum strongly coupled ${\mathcal{N}}=4$ SU(N) superconformal gauge theory. We extend this result and calculate entanglement entropy of a generic 4d conformal field theory. As a byproduct, we obtain a closed-form expression for the entanglement entropy in flat space-time when $Σ$ is sphere $S_2$ and when $Σ$ is two-dimensional cylinder. The contribution of the type A conformal anomaly to entanglement entropy is always determined by topology of surface $Σ$ while the dependence of the entropy on the extrinsic geometry of $Σ$ is due to the type B conformal anomaly.

hep-th↗

arXiv2008

Black Hole Entropy and Gravity Cutoff

We study the black hole entropy as entanglement entropy and propose a resolution to the species puzzle. This resolution comes out naturally due to the fact that in the presence of $N$ species the universal gravitational cutoff is $Λ=M_{\rm Planck}/\sqrt{N}$, as opposed to $M_{\rm Planck}$. We demonstrate consistency of our solution by showing the equality of the two entropies in explicit examples in which the relation between $M_{\rm Planck}$ and $Λ$ is known from the fundamental theory.

hep-th↗

arXiv2007

Wormholes as Black Hole Foils

We study to what extent wormholes can mimic the observational features of black holes. It is surprisingly found that many features that could be thought of as ``characteristic'' of a black hole (endowed with an event horizon) can be closely mimicked by a globally static wormhole, having no event horizon. This is the case for: the apparently irreversible accretion of matter down a hole, no-hair properties, quasi-normal-mode ringing, and even the dissipative properties of black hole horizons, such as a finite surface resistivity equal to 377 Ohms. The only way to distinguish the two geometries on an observationally reasonable time scale would be through the detection of Hawking's radiation, which is, however, too weak to be of practical relevance for astrophysical black holes. We point out the existence of an interesting spectrum of quantum microstates trapped in the throat of a wormhole which could be relevant for storing the information ``lost'' during a gravitational collapse.

gr-qc↗

arXiv2006

Entanglement entropy of black holes and AdS/CFT correspondence

A recent proposal by Ryu and Takayanagi for a holographic interpretation of entanglement entropy in conformal field theories dual to supergravity on anti-de Sitter (adS) is generalized to include entanglement entropy of black holes living on the boundary of adS. The generalized proposal is verified in boundary dimensions $d=2$ and $d=4$ for both the UV divergent and UV finite terms. In dimension $d=4$ an expansion of entanglement entropy in terms of size $L$ of the subsystem outside the black hole is considered. A new term in the entropy of dual strongly coupled CFT, which universally grows as $L^2\ln L$ and is proportional to the value of the obstruction tensor at the black hole horizon, is predicted.

hep-th↗

arXiv2006

Entanglement entropy and the Ricci flow

We analyze the Ricci flow of a noncompact metric that describes a two-dimensional black hole. We consider entanglement entropy of a 2d black hole which is due to the quantum correlations between two subsystems: one is inside and the other is outside the black hole horizon. It is demonstrated that the entanglement entropy is monotonic along the Ricci flow.

hep-th↗

arXiv2006

Holographic Description of Gravitational Anomalies

The holographic duality can be extended to include quantum theories with broken coordinate invariance leading to the appearance of the gravitational anomalies. On the gravity side one adds the gravitational Chern-Simons term to the bulk action which gauge invariance is only up to the boundary terms. We analyze in detail how the gravitational anomalies originate from the modified Einstein equations in the bulk. As a side observation we find that the gravitational Chern-Simons functional has interesting conformal properties. It is invariant under conformal transformations. Moreover, its metric variation produces conformal tensor which is a generalization of the Cotton tensor to dimension $d+1=4k-1, k\in Z$. We calculate the modification of the holographic stress-energy tensor that is due to the Chern-Simons term and use the bulk Einstein equations to find its divergence and thus reproduce the gravitational anomaly. Explicit calculation of the anomaly is carried out in dimensions $d=2$ and $d=6$. The result of the holographic calculation is compared with that of the descent method and agreement is found. The gravitational Chern-Simons term originates by Kaluza-Klein mechanism from a one-loop modification of M-theory action. This modification is discussed in the context of the gravitational anomaly in six-dimensional $(2,0)$ theory. The agreement with earlier conjectured anomaly is found.

hep-th↗

arXiv2005

Holography with Gravitational Chern-Simons Term

The holographic description in the presence of gravitational Chern-Simons term is studied. The modified gravitational equations are integrated by using the Fefferman-Graham expansion and the holographic stress-energy tensor is identified. The stress-energy tensor has both conformal anomaly and gravitational or, if re-formulated in terms of the zweibein, Lorentz anomaly. We comment on the structure of anomalies in two dimensions and show that the two-dimensional stress-energy tensor can be reproduced by integrating the conformal and gravitational anomalies. We study the black hole entropy in theories with a gravitational Chern-Simons term and find that the usual Bekenstein-Hawking entropy is modified. For the BTZ black hole the modification is determined by area of the inner horizon. We show that the total entropy of the BTZ black hole is precisely reproduced in a boundary CFT calculation using the Cardy formula.

hep-th↗

arXiv2005

Restoring Unitarity in BTZ Black Hole

Whether or not system is unitary can be seen from the way it, if perturbed, relaxes back to equilibrium. The relaxation of semiclassical black hole can be described in terms of correlation function which exponentially decays with time. In the momentum space it is represented by infinite set of complex poles to be identified with the quasi-normal modes. This behavior is in sharp contrast to the relaxation in unitary theory in finite volume: correlation function of the perturbation in this case is quasi-periodic function of time and, in general, is expected to show the Poincaré recurrences. In this paper we demonstrate how restore unitarity in the BTZ black hole, the simplest example of eternal black hole in finite volume. We start with reviewing the relaxation in the semiclassical BTZ black hole and how this relaxation is mirrored in the boundary conformal field theory as suggested by the AdS/CFT correspondence. We analyze the sum over $SL(2,{\bf Z})$ images of the BTZ space-time and suggest that it does not produce a quasi-periodic relaxation, as one might have hoped, but results in correlation function which decays by power law. We develop our earlier suggestion and consider a non-semiclassical deformation of the BTZ space-time that has structure of wormhole connecting two asymptotic regions semiclassically separated by horizon. The small deformation parameter $λ$ is supposed to have non-perturbative origin to capture the finite N behavior of the boundary theory. The discrete spectrum of perturbation in the modified space-time is computed and is shown to determine the expected unitary behavior: the corresponding time evolution is quasi-periodic with hierarchy of large time scales $\ln 1/λ$ and $1/λ$ interpreted respectively as the Heisenberg and Poincaré time scales in the system.

hep-th↗

arXiv2004

Reconstructing Minkowski Space-Time

Minkowski space is a physically important space-time for which the finding an adequate holographic description is an urgent problem. In this paper we develop further the proposal made in hep-th/0303006 for the description as a duality between Minkowski space-time and a Conformal Field Theory defined on the boundary of the light-cone. We focus on the gravitational aspects of the duality. Specifically, we identify the gravitational holographic data and provide the way Minkowski space-time (understood in more general context as a Ricci-flat space) is reconstructed from the data. In order to avoid the complexity of non-linear Einstein equations we consider linear perturbations and do the analysis for the perturbations. The analysis proceeds in two steps. We first reduce the problem in Minkowski space to an infinite set of field equations on de Sitter space one dimension lower. These equations are quite remarkable: they describe massless and massive gravitons in de Sitter space. In particular, the partially massless graviton appears naturally in this reduction. In the second step we solve the graviton field equations and identify the holographic boundary data. Finally, we consider the asymptotic form of the black hole space-time and identify the way the information about the mass of the static gravitational configuration is encoded in the holographic data.

hep-th↗

arXiv2004

Can Black Hole Relax Unitarily?

We review the way the BTZ black hole relaxes back to thermal equilibrium after a small perturbation and how it is seen in the boundary (finite volume) CFT. The unitarity requires the relaxation to be quasi-periodic. It is preserved in the CFT but is not obvious in the case of the semiclassical black hole the relaxation of which is driven by complex quasi-normal modes. We discuss two ways of modifying the semiclassical black hole geometry to maintain unitarity: the (fractal) brick wall and the worm-hole modification. In the latter case the entropy comes out correctly as well.

hep-th↗

arXiv2004

Effective Stringy Description of Schwarzschild Black Holes

We start by pointing out that certain Riemann surfaces appear rather naturally in the context of wave equations in the black hole background. For a given black hole there are two closely related surfaces. One is the Riemann surface of complexified ``tortoise'' coordinate. The other Riemann surface appears when the radial wave equation is interpreted as the Fuchsian differential equation. We study these surfaces in detail for the BTZ and Schwarzschild black holes in four and higher dimensions. Topologically, in all cases both surfaces are a sphere with a set of marked points; for BTZ and 4D Schwarzschild black holes there is 3 marked points. In certain limits the surfaces can be characterized very explicitly. We then show how properties of the wave equation (quasi-normal modes) in such limits are encoded in the geometry of the corresponding surfaces. In particular, for the Schwarzschild black hole in the high damping limit we describe the Riemann surface in question and use this to derive the quasi-normal mode frequencies with the log(3) as the real part. We then argue that the surfaces one finds this way signal an appearance of an effective string. We propose that a description of this effective string propagating in the black hole background can be given in terms of the Liouville theory living on the corresponding Riemann surface. We give such a stringy description for the Schwarzschild black hole in the limit of high damping and show that the quasi-normal modes emerge naturally as the poles in 3-point correlation function in the effective conformal theory.

hep-th↗

arXiv2003

Horizon State, Hawking Radiation and Boundary Liouville Model

We demonstrate that the near-horizon physics, the Hawking radiation and the reflection off the radial potential barrier, can be understood entirely within a conformal field theory picture in terms of one- and two-point functions in the boundary Liouville theory. An important element in this demonstration is the notion of {\it horizon state}, the Hawking radiation being interpreted as a result of the transition of horizon state to the ordinary states propagating outside black hole horizon.

hep-th↗