21 research outputs found
Fast Scramblers Of Small Size
We investigate various geometrical aspects of the notion of `optical depth'
in the thermal atmosphere of black hole horizons. Optical depth has been
proposed as a measure of fast-crambling times in such black hole systems, and
the associated optical metric suggests that classical chaos plays a leading
role in the actual scrambling mechanism. We study the behavior of the optical
depth with the size of the system and find that AdS/CFT phase transitions with
topology change occur naturally as the scrambler becomes smaller than its
thermal length. In the context of detailed AdS/CFT models based on D-branes,
T-duality implies that small scramblers are described in terms of matrix
quantum mechanics.Comment: 14 pages, 3 figures. Added reference
Holography of AdS vacuum bubbles
We consider the fate of AdS vacua connected by tunneling events. A precise
holographic dual of thin-walled Coleman--de Luccia bounces is proposed in terms
of Fubini instantons in an unstable CFT. This proposal is backed by several
qualitative and quantitative checks, including the precise calculation of the
instanton action appearing in evaluating the decay rate. Big crunches manifest
themselves as time dependent processes which reach the boundary of field space
in a finite time. The infinite energy difference involved is identified on the
boundary and highlights the ill-defined nature of the bulk setup. We propose a
qualitative scenario in which the crunch is resolved by stabilizing the CFT, so
that all attempts at crunching always end up shielded from the boundary by the
formation of black hole horizons. In all these well defined bulk processes the
configurations have the same asymptotics and are finite energy excitations.Comment: version submitted to journal. Note added referring to previous work
on holographic instantons
Quasinormal modes and holographic correlators in a crunching AdS geometry
We calculate frequency space holographic correlators in an asymptotically AdS crunching background, dual to a relevant deformation of the M2-brane CFT placed in de Sitter spacetime. For massless bulk scalars, exploiting the connection to a solvable supersymmetric quantum mechanical problem, we obtain the exact frequency space correlator for the dual operator in the deformed CFT. Controlling the shape of the crunching surface in the Penrose diagram by smoothly dialling the deformation from zero to infinity, we observe that in the large deformation limit the Penrose diagram becomes a `square', and the exact holographic correlators display striking similarities to their counterparts in the BTZ black hole and its higher dimensional generalisations. We numerically determine quasinormal poles for relevant and irrelevant operators, and find an intricate pattern of these in the complex frequency plane. In the case of relevant operators, the deformation parameter has an infinite sequence of critical values, each one characterised by a pair of poles colliding and moving away from the imaginary frequency axis with increasing deformation. In the limit of infinite deformation all scalar operators have identical quasinormal spectra. We compare and contrast our strongly coupled de Sitter QFT results with strongly coupled thermal correlators from AdS black holes
Probing crunching AdS cosmologies
Holographic gravity duals of deformations of CFTs formulated on de Sitter spacetime contain FRW geometries behind a horizon, with cosmological big crunch singularities. Using a specific analytically tractable solution within a particular single scalar truncation of N=8 supergravity on AdS_4, we first probe such crunching cosmologies with spacelike radial geodesics that compute spatially antipodal correlators of large dimension boundary operators. At late times, the geodesics lie on the FRW slice of maximal expansion behind the horizon. The late time two-point functions factorise, and when transformed to the Einstein static universe, they exhibit a temporal non-analyticity determined by the maximal value of the scale factor a_max. Radial geodesics connecting antipodal points necessarily have de Sitter energy E < a_max, while geodesics with E > a_max terminate at the crunch, the two categories of geodesics being separated by the maximal expansion slice.The spacelike crunch singularity is curved ``outward'' in the Penrose diagram for the deformed AdS backgrounds, and thus geodesic limits of the antipodal correlators do not directly probe the crunch. Beyond the geodesic limit, we point out that the scalar wave equation, analytically continued into the FRW patch, has a potential which is singular at the crunch along with complex WKB turning points in the vicinity of the FRW crunch. We then argue that the frequency space Green's function has a branch point determined by a_max which corresponds to the lowest quasinormal frequency
Entanglement entropy of black holes
The entanglement entropy is a fundamental quantity which characterizes the
correlations between sub-systems in a larger quantum-mechanical system. For two
sub-systems separated by a surface the entanglement entropy is proportional to
the area of the surface and depends on the UV cutoff which regulates the
short-distance correlations. The geometrical nature of the entanglement entropy
calculation is particularly intriguing when applied to black holes when the
entangling surface is the black hole horizon. I review a variety of aspects of
this calculation: the useful mathematical tools such as the geometry of spaces
with conical singularities and the heat kernel method, the UV divergences in
the entropy and their renormalization, the logarithmic terms in the
entanglement entropy in 4 and 6 dimensions and their relation to the conformal
anomalies. The focus in the review is on the systematic use of the conical
singularity method. The relations to other known approaches such as 't Hooft's
brick wall model and the Euclidean path integral in the optical metric are
discussed in detail. The puzzling behavior of the entanglement entropy due to
fields which non-minimally couple to gravity is emphasized. The holographic
description of the entanglement entropy of the black hole horizon is
illustrated on the two- and four-dimensional examples. Finally, I examine the
possibility to interpret the Bekenstein-Hawking entropy entirely as the
entanglement entropy.Comment: 89 pages; an invited review to be published in Living Reviews in
Relativit