11 research outputs found
Cosmological Topologically Massive Gravitons and Photons
We study topologically massive (2+1)-dimensional gravity with a negative
cosmological constant. The masses of the linearized curvature excitations about
AdS_3 backgrounds are not only shifted from their flat background values but,
more surprisingly, split according to chirality. For all finite values of the
topological mass, we find a single bulk degree of freedom with positive energy,
and exhibit a complete set of normalizable, finite-energy wave packet
solutions. This model can also be written as a sum of two higher-derivative
SL(2,R) Chern--Simons theories, weighted by the central charges of the boundary
conformal field theory. At two particular "critical" values of the couplings,
one of these central charges vanishes, and linearized topologically massive
gravity becomes equivalent to topologically massive electromagnetism; however,
the physics of the bulk wave packets remains unaltered here.Comment: 36 pages, 1 figure. v2: Expanded; exhibits localized normalizable
wave packets and exact chiral pp-wave solutions. v3: Added references;
clarification on bulk vs. boundary chirality. v4: Published version; changes
include discussion of bulk solutions' asymptotic acceptability at all m
The General Supersymmetric Solution of Topologically Massive Supergravity
We find the general fully non-linear solution of topologically massive
supergravity admitting a Killing spinor. It is of plane-wave type, with a null
Killing vector field. Conversely, we show that all solutions with a null
Killing vector are supersymmetric for one or the other choice of sign for the
Chern-Simons coupling constant \mu. If \mu does not take the critical value
\mu=\pm 1, these solutions are asymptotically regular on a Poincar\'e patch,
but do not admit a smooth global compactification with boundary S^1\times\R. In
the critical case, the solutions have a logarithmic singularity on the boundary
of the Poincar\'e patch. We derive a Nester-Witten identity, which allows us to
identify the associated charges, but we conclude that the presence of the
Chern-Simons term prevents us from making a statement about their positivity.
The Nester-Witten procedure is applied to the BTZ black hole.Comment: Minor correction
Topologically Massive Gravity and Ricci-Cotton Flow
We consider Topologically Massive Gravity (TMG), which is three dimensional
general relativity with a cosmological constant and a gravitational
Chern-Simons term. When the cosmological constant is negative the theory has
two potential vacuum solutions: Anti-de Sitter space and Warped Anti-de Sitter
space. The theory also contains a massive graviton state which renders these
solutions unstable for certain values of the parameters and boundary
conditions. We study the decay of these solutions due to the condensation of
the massive graviton mode using Ricci-Cotton flow, which is the appropriate
generalization of Ricci flow to TMG. When the Chern-Simons coupling is small
the AdS solution flows to warped AdS by the condensation of the massive
graviton mode. When the coupling is large the situation is reversed, and warped
AdS flows to AdS. Minisuperspace models are constructed where these flows are
studied explicitly
Warped AdS_3 Black Holes
Three dimensional topologically massive gravity (TMG) with a negative
cosmological constant -\ell^{-2} and positive Newton constant G admits an AdS_3
vacuum solution for any value of the graviton mass \mu. These are all known to
be perturbatively unstable except at the recently explored chiral point
\mu\ell=1. However we show herein that for every value of \mu\ell< 3 there are
two other (potentially stable) vacuum solutions given by SL(2,R)x
U(1)-invariant warped AdS_3 geometries, with a timelike or spacelike U(1)
isometry.
Critical behavior occurs at \mu\ell=3, where the warping transitions from a
stretching to a squashing, and there are a pair of warped solutions with a null
U(1) isometry. For \mu\ell>3, there are known warped black hole solutions which
are asymptotic to warped AdS_3. We show that these black holes are discrete
quotients of warped AdS_3 just as BTZ black holes are discrete quotients of
ordinary AdS_3. Moreover new solutions of this type, relevant to any theory
with warped AdS_3 solutions, are exhibited. Finally we note that the black hole
thermodynamics is consistent with the hypothesis that, for \mu\ell>3, the
warped AdS_3 ground state of TMG is holographically dual to a 2D boundary CFT
with central charges c_R={15(\mu\ell)^2+81\over G\mu((\mu\ell)^2+27)} and
c_L={12 \mu\ell^2\over G((\mu\ell)^2+27)}.Comment: 29 page
Black holes with a null Killing vector in three-dimensional massive gravity
We investigate solutions of new massive gravity with two commuting Killing
vectors, one of which is null, with a special emphasis on black hole solutions.
Besides extreme BTZ black holes and, for a special value of the coupling
constant, massless null warped black holes, we also obtain for a critical
coupling a family of massive "log" black holes. These are asymptotic to the
extreme BTZ black holes in the sense of log gravity.Comment: 16 pages; v2: title changed; v3: section 4 reworked; version to be
published in Classical and Quantum Gravit
Holographic Entanglement Entropy: An Overview
In this article, we review recent progresses on the holographic
understandings of the entanglement entropy in the AdS/CFT correspondence. After
reviewing the general idea of holographic entanglement entropy, we will explain
its applications to confinement/deconfinement phase transitions, black hole
entropy and covariant formulation of holography.Comment: 52 pages, Invited review article for a special issue "Entanglement
entropy in extended quantum systems" in Journal of Physics A, edited by
P.Calabrese, J. Cardy and B. Doyon; (v2) references adde