336 research outputs found
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 and for both the UV divergent and UV finite
terms. In dimension an expansion of entanglement entropy in terms of size
of the subsystem outside the black hole is considered. A new term in the
entropy of dual strongly coupled CFT, which universally grows as and
is proportional to the value of the obstruction tensor at the black hole
horizon, is predicted.Comment: 5 pages; minor typos corrected, minor changes in text. Version
accepted for publication in Phys. Rev. Let
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.Comment: 19 pages, Latex; v3: minor corrections, some clarification
Holographic (De)confinement Transitions in Cosmological Backgrounds
For type IIB supergravity with a running axio-dilaton, we construct bulk
solutions which admit a cosmological background metric of
Friedmann-Robertson-Walker type. These solutions include both a dark radiation
term in the bulk as well as a four-dimensional (boundary) cosmological
constant, while gravity at the boundary remains non-dynamical. We
holographically calculate the stress-energy tensor, showing that it consists of
two contributions: The first one, generated by the dark radiation term, leads
to the thermal fluid of N = 4 SYM theory, while the second, the conformal
anomaly, originates from the boundary cosmological constant. Conservation of
the boundary stress tensor implies that the boundary cosmological constant is
time-independent, such that there is no exchange between the two stress-tensor
contributions. We then study (de)confinement by evaluating the Wilson loop in
these backgrounds. While the dark radiation term favours deconfinement, a
negative cosmological constant drives the system into a confined phase. When
both contributions are present, we find an oscillating universe with negative
cosmological constant which undergoes periodic (de)confinement transitions as
the scale of three space expands and re-contracts.Comment: 31 pages, 5 figures, v2: Reference adde
Cosmology from an AdS Schwarzschild black hole via holography
We derive the equations of cosmological evolution from an AdS Schwarzschild
black hole via holographic renormalization with appropriate boundary
conditions.Comment: 6 page
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.Comment: 15 pages, no figures; v.2: conjecture 1 on p. 11 made more precise;
version published in jhe
A classification of local Weyl invariants in D=8
Following a purely algebraic procedure, we provide an exhaustive
classification of local Weyl-invariant scalar densities in dimension D=8.Comment: LaTeX, 19 pages, typos corrected, one reference adde
Late time solutions for inhomogeneous Lambda-CDM cosmology, their characterization and observation
Assuming homogeneous isotropic Lambda-CDM cosmology allows Lambda, spatial
curvature and dark matter density to be inferred from large scale structure
observations such as supernovae. The purpose of this paper is to extend this to
allow observations to measure or constrain inhomogeneity and anisotropy. We
obtain the general inhomogeneous anisotropic Lambda-CDM solution which is
locally asymptotic to an expanding de Sitter solution as a late time expansion
using Starobinsky's method (analogous to the `holographic renormalization'
technique in AdS/CFT) together with a resummation of the series. The dark
matter is modeled as perfect dust fluid. The terms in the expansion
systematically describe inhomogeneous and anisotropic deformations of an
expanding FLRW solution, and are given as a spatial derivative expansion in
terms of data characterizing the solution - a 3-metric and a perturbation of
that 3-metric. Leading terms describe inhomogeneity and anisotropy on the scale
set by the cosmological constant, approximately the horizon scale today. Higher
terms in the expansion describe shorter scale variations. We compute the
luminosity distance-redshift relation and argue that comparison with current
and future observation would allow a partial reconstruction of the
characterizing data. We also comment on smoothing these solutions noting that
geometric flows (such as Ricci flow) applied to the characterizing data provide
a canonical averaging method.Comment: 15 pages, 2 figures; v2: minor corrections and improvements,
references adde
Compactifications of conformal gravity
We study conformal theories of gravity, i.e. those whose action is invariant
under the local transformation g_{\mu\nu} -> \omega^2 (x) g_{\mu\nu}. As is
well known, in order to obtain Einstein gravity in 4D it is necessary to
introduce a scalar compensator with a VEV that spontaneously breaks the
conformal invariance and generates the Planck mass. We show that the
compactification of extra dimensions in a higher dimensional conformal theory
of gravity also yields Einstein gravity in lower dimensions, without the need
to introduce the scalar compensator. It is the field associated with the size
of the extra dimensions (the radion) who takes the role of the scalar
compensator in 4D. The radion has in this case no physical excitations since
they are gauged away in the Einstein frame for the metric. In these models the
stabilization of the size of the extra dimensions is therefore automatic.Comment: 13 page
Gravity, Two Times, Tractors, Weyl Invariance and Six Dimensional Quantum Mechanics
Fefferman and Graham showed some time ago that four dimensional conformal
geometries could be analyzed in terms of six dimensional, ambient, Riemannian
geometries admitting a closed homothety. Recently it was shown how conformal
geometry provides a description of physics manifestly invariant under local
choices of unit systems. Strikingly, Einstein's equations are then equivalent
to the existence of a parallel scale tractor (a six component vector subject to
a certain first order covariant constancy condition at every point in four
dimensional spacetime). These results suggest a six dimensional description of
four dimensional physics, a viewpoint promulgated by the two times physics
program of Bars. The Fefferman--Graham construction relies on a triplet of
operators corresponding, respectively to a curved six dimensional light cone,
the dilation generator and the Laplacian. These form an sp(2) algebra which
Bars employs as a first class algebra of constraints in a six-dimensional gauge
theory. In this article four dimensional gravity is recast in terms of six
dimensional quantum mechanics by melding the two times and tractor approaches.
This "parent" formulation of gravity is built from an infinite set of six
dimensional fields. Successively integrating out these fields yields various
novel descriptions of gravity including a new four dimensional one built from a
scalar doublet, a tractor vector multiplet and a conformal class of metrics.Comment: 27 pages, LaTe
Smooth extensions of functions on separable Banach spaces
Let be a Banach space with a separable dual . Let be
a closed subspace, and a -smooth function. Then we
show there is a extension of to .Comment: 19 pages. This version fixes a gap in the previous proof of Theorem 1
by providing a sharp version of Lemma
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