37 research outputs found
The Gravity Dual of a Density Matrix
For a state in a quantum field theory on some spacetime, we can associate a
density matrix to any subset of a given spacelike slice by tracing out the
remaining degrees of freedom. In the context of the AdS/CFT correspondence, if
the original state has a dual bulk spacetime with a good classical description,
it is natural to ask how much information about the bulk spacetime is carried
by the density matrix for such a subset of field theory degrees of freedom. In
this note, we provide several constraints on the largest region that can be
fully reconstructed, and discuss specific proposals for the geometric
construction of this dual region.Comment: 19 pages, LaTeX, 8 figures, v2: footnote and reference adde
Holographic models of de Sitter QFTs
We describe the dynamics of strongly coupled field theories in de Sitter
spacetime using the holographic gauge/gravity duality. The main motivation for
this is to explore the possibility of dynamical phase transitions during
cosmological evolution. Specifically, we study two classes of theories: (i)
conformal field theories on de Sitter in the static patch which are maintained
in equilibrium at temperatures that may differ from the de Sitter temperature
and (ii) confining gauge theories on de Sitter spacetime. In the former case we
show the such states make sense from the holographic viewpoint in that they
have regular bulk gravity solutions. In the latter situation we add to the
evidence for a confinement/deconfinement transition for a large N planar gauge
theory as the cosmological acceleration is increased past a critical value. For
the field theories we study, the critical acceleration corresponds to a de
Sitter temperature which is less than the Minkowski space deconfinement
transition temperature by a factor of the spacetime dimension.Comment: 35 pages, LaTeX, 4 figures, v2: refs adde
A note on spherically symmetric naked singularities in general dimension
We discuss generalizations of the recent theorem by Dafermos (hep-th/0403033)
forbidding a certain class of naked singularities in the spherical collapse of
a scalar field. Employing techniques similar to the ones Dafermos used, we
consider extending the theorem (1) to higher dimensions, (2) by including more
general matter represented by a stress-energy tensor satisfying certain
assumptions, and (3) by replacing the spherical geometry by a toroidal or
higher genus (locally hyperbolic) one. We show that the extension to higher
dimensions and a more general topology is straightforward; on the other hand,
replacing the scalar field by a more general matter content forces us to shrink
the class of naked singularities we are able to exclude. We then show that the
most common matter theories (scalar field interacting with a non-abelian gauge
field and a perfect fluid satisfying certain conditions) obey the assumptions
of our weaker theorem, and we end by commenting on the applicability of our
results to the five-dimensional AdS scenarii considered recently in the
literature.Comment: 16 pages, no figures, typos fixe
Bi-partite entanglement entropy in integrable models with backscattering
In this paper we generalise the main result of a recent work by J. L. Cardy
and the present authors concerning the bi-partite entanglement entropy between
a connected region and its complement. There the expression of the leading
order correction to saturation in the large distance regime was obtained for
integrable quantum field theories possessing diagonal scattering matrices. It
was observed to depend only on the mass spectrum of the model and not on the
specific structure of the diagonal scattering matrix. Here we extend that
result to integrable models with backscattering (i.e. with non-diagonal
scattering matrices). We use again the replica method, which connects the
entanglement entropy to partition functions on Riemann surfaces with two branch
points. Our main conclusion is that the mentioned infrared correction takes
exactly the same form for theories with and without backscattering. In order to
give further support to this result, we provide a detailed analysis in the
sine-Gordon model in the coupling regime in which no bound states (breathers)
occur. As a consequence, we obtain the leading correction to the sine-Gordon
partition function on a Riemann surface in the large distance regime.
Observations are made concerning the limit of large number of sheets.Comment: 22 pages, 2 figure
The Kerr-Newman-Godel Black Hole
By applying a set of Hassan-Sen transformations and string dualities to the
Kerr-Godel solution of minimal D=5 supergravity we derive a four parameter
family of five dimensional solutions in type II string theory. They describe
rotating, charged black holes in a rotating background. For zero background
rotation, the solution is D=5 Kerr-Newman; for zero charge it is Kerr-Godel. In
a particular extremal limit the solution describes an asymptotically Godel BMPV
black hole.Comment: 12 pages, LaTeX, no figures; v2: one reference added, very minor
changes; to appear in CQ
Brownian motion in AdS/CFT
We study Brownian motion and the associated Langevin equation in AdS/CFT. The
Brownian particle is realized in the bulk spacetime as a probe fundamental
string in an asymptotically AdS black hole background, stretching between the
AdS boundary and the horizon. The modes on the string are excited by the
thermal black hole environment and consequently the string endpoint at the
boundary undergoes an erratic motion, which is identified with an external
quark in the boundary CFT exhibiting Brownian motion. Semiclassically, the
modes on the string are thermally excited due to Hawking radiation, which
translates into the random force appearing in the boundary Langevin equation,
while the friction in the Langevin equation corresponds to the excitation on
the string being absorbed by the black hole. We give a bulk proof of the
fluctuation-dissipation theorem relating the random force and friction. This
work can be regarded as a step toward understanding the quantum microphysics
underlying the fluid-gravity correspondence. We also initiate a study of the
properties of the effective membrane or stretched horizon picture of black
holes using our bulk description of Brownian motion.Comment: 54 pages (38 pages + 5 appendices), 5 figures. v2: references added,
clarifications in 6.2. v3: clarifications, version submitted to JHE
Entanglement Entropy from a Holographic Viewpoint
The entanglement entropy has been historically studied by many authors in
order to obtain quantum mechanical interpretations of the gravitational
entropy. The discovery of AdS/CFT correspondence leads to the idea of
holographic entanglement entropy, which is a clear solution to this important
problem in gravity. In this article, we would like to give a quick survey of
recent progresses on the holographic entanglement entropy. We focus on its
gravitational aspects, so that it is comprehensible to those who are familiar
with general relativity and basics of quantum field theory.Comment: Latex, 30 pages, invited review for Classical and Quantum Gravity,
minor correction
Ricci solitons, Ricci flow, and strongly coupled CFT in the Schwarzschild Unruh or Boulware vacua
The elliptic Einstein-DeTurck equation may be used to numerically find
Einstein metrics on Riemannian manifolds. Static Lorentzian Einstein metrics
are considered by analytically continuing to Euclidean time. Ricci-DeTurck flow
is a constructive algorithm to solve this equation, and is simple to implement
when the solution is a stable fixed point, the only complication being that
Ricci solitons may exist which are not Einstein. Here we extend previous work
to consider the Einstein-DeTurck equation for Riemannian manifolds with
boundaries, and those that continue to static Lorentzian spacetimes which are
asymptotically flat, Kaluza-Klein, locally AdS or have extremal horizons. Using
a maximum principle we prove that Ricci solitons do not exist in these cases
and so any solution is Einstein. We also argue that Ricci-DeTurck flow
preserves these classes of manifolds. As an example we simulate Ricci-DeTurck
flow for a manifold with asymptotics relevant for AdS_5/CFT_4. Our maximum
principle dictates there are no soliton solutions, and we give strong numerical
evidence that there exists a stable fixed point of the flow which continues to
a smooth static Lorentzian Einstein metric. Our asymptotics are such that this
describes the classical gravity dual relevant for the CFT on a Schwarzschild
background in either the Unruh or Boulware vacua. It determines the leading
O(N^2) part of the CFT stress tensor, which interestingly is regular on both
the future and past Schwarzschild horizons.Comment: 48 pages, 7 figures; Version 2 - section 2.2.1 on manifolds with
boundaries substantially modified, corrected and extended. Discussion in
section 3.1 amended. References added and minor change