53 research outputs found
Holographic formula for the determinant of the scattering operator in thermal AdS
A 'holographic formula' expressing the functional determinant of the
scattering operator in an asymptotically locally anti-de Sitter(ALAdS) space
has been proposed in terms of a relative functional determinant of the scalar
Laplacian in the bulk. It stems from considerations in AdS/CFT correspondence
of a quantum correction to the partition function in the bulk and the
corresponding subleading correction at large N on the boundary. In this paper
we probe this prediction for a class of quotients of hyperbolic space by a
discrete subgroup of isometries. We restrict to the simplest situation of an
abelian group where the quotient geometry describes thermal AdS and also the
non-spinning BTZ instanton. The bulk computation is explicitly done using the
method of images and the answer can be encoded in a (Patterson-)Selberg
zeta-function.Comment: 11 pages, published JPA versio
Remarks on evolution of space-times in 3+1 and 4+1 dimensions
A large class of vacuum space-times is constructed in dimension 4+1 from
hyperboloidal initial data sets which are not small perturbations of empty
space data. These space-times are future geodesically complete, smooth up to
their future null infinity, and extend as vacuum space-times through their
Cauchy horizon. Dimensional reduction gives non-vacuum space-times with the
same properties in 3+1 dimensions.Comment: 10pp, exposition improved; final versio
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
Gravity in the 3+1-Split Formalism II: Self-Duality and the Emergence of the Gravitational Chern-Simons in the Boundary
We study self-duality in the context of the 3+1-split formalism of gravity
with non-zero cosmological constant. Lorentzian self-dual configurations are
conformally flat spacetimes and have boundary data determined by classical
solutions of the three-dimensional gravitational Chern-Simons. For Euclidean
self-dual configurations, the relationship between their boundary initial
positions and initial velocity is also determined by the three-dimensional
gravitational Chern-Simons. Our results imply that bulk self-dual
configurations are holographically described by the gravitational Chern-Simons
theory which can either viewed as a boundary generating functional or as a
boundary effective action.Comment: 25 pages; v2: minor improvements, references adde
Gravity in the 3+1-Split Formalism I: Holography as an Initial Value Problem
We present a detailed analysis of the 3+1-split formalism of gravity in the
presence of a cosmological constant. The formalism helps revealing the intimate
connection between holography and the initial value formulation of gravity. We
show that the various methods of holographic subtraction of divergences
correspond just to different transformations of the canonical variables, such
that the initial value problem is properly set up at the boundary. The
renormalized boundary energy momentum tensor is a component of the Weyl tensor.Comment: 28 pages; v2: minor improvements, references adde
Diffeomorphisms and Holographic Anomalies
Using the relation between diffeomorphisms in the bulk and Weyl
transformations on the boundary we study the Weyl transformation properties of
the bulk metric on shell and of the boundary action. We obtain a universal
formula for one of the classes of trace anomalies in any even dimension in
terms of the parameters of the gravity action.Comment: 12 pages, harvma
The CFT dual of AdS gravity with torsion
We consider the Mielke-Baekler model of three-dimensional AdS gravity with
torsion, which has gravitational and translational Chern-Simons terms in
addition to the usual Einstein-Hilbert action with cosmological constant. It is
shown that the topological nature of the model leads to a finite
Fefferman-Graham expansion. We derive the holographic stress tensor and the
associated Ward identities and show that, due to the asymmetry of the left- and
right-moving central charges, a Lorentz anomaly appears in the dual conformal
field theory. Both the consistent and the covariant Weyl and Lorentz anomaly
are determined, and the Wess-Zumino consistency conditions for the former are
verified. Moreover we consider the most general solution with flat boundary
geometry, which describes left-and right-moving gravitational waves on AdS_3
with torsion, and shew that in this case the holographic energy-momentum tensor
is given by the wave profiles. The anomalous transformation laws of the wave
profiles under diffeomorphisms preserving the asymptotic form of the bulk
solution yield the central charges of the dual CFT and confirm the results that
appeared earlier on in the literature. We finally comment on some points
concerning the microstate counting for the Riemann-Cartan black hole.Comment: 17 pages, uses JHEP3.cls. References added, minor errors correcte
Determinant and Weyl anomaly of Dirac operator: a holographic derivation
We present a holographic formula relating functional determinants: the
fermion determinant in the one-loop effective action of bulk spinors in an
asymptotically locally AdS background, and the determinant of the two-point
function of the dual operator at the conformal boundary. The formula originates
from AdS/CFT heuristics that map a quantum contribution in the bulk partition
function to a subleading large-N contribution in the boundary partition
function. We use this holographic picture to address questions in spectral
theory and conformal geometry. As an instance, we compute the type-A Weyl
anomaly and the determinant of the iterated Dirac operator on round spheres,
express the latter in terms of Barnes' multiple gamma function and gain insight
into a conjecture by B\"ar and Schopka.Comment: 11 pages; new comments and references added, typos correcte
Conserved Charges in Even Dimensional Asymptotically locally Anti-de Sitter Space-times
Based on the recent paper hep-th/0503045, we derive a formula of calculating
conserved charges in even dimensional asymptotically {\it locally} anti-de
Sitter space-times by using the definition of Wald and Zoupas. This formula
generalizes the one proposed by Ashtekar {\it et al}. Using the new formula we
compute the masses of Taub-Bolt-AdS space-times by treating Taub-Nut-AdS
space-times as the reference solution. Our result agrees with those resulting
from "background subtraction" method or "boundary counterterm" method. We also
calculate the conserved charges of Kerr-Taub-Nut-AdS solutions in four
dimensions and higher dimensional Kerr-AdS solutions with Nut charges. The mass
of (un)wrapped brane solutions in any dimension is given.Comment: Latex, 28 pages, v2: minor changes, to appear in JHE
Schr\"odinger Manifolds
This article propounds, in the wake of influential work of Fefferman and
Graham about Poincar\'e extensions of conformal structures, a definition of a
(Poincar\'e-)Schr\"odinger manifold whose boundary is endowed with a conformal
Bargmann structure above a non-relativistic Newton-Cartan spacetime. Examples
of such manifolds are worked out in terms of homogeneous spaces of the
Schr\"odinger group in any spatial dimension, and their global topology is
carefully analyzed. These archetypes of Schr\"odinger manifolds carry a Lorentz
structure together with a preferred null Killing vector field; they are shown
to admit the Schr\"odinger group as their maximal group of isometries. The
relationship to similar objects arising in the non-relativisitc AdS/CFT
correspondence is discussed and clarified.Comment: 42 pages, 1 figure, published version: J. Phys. A: Math. Theor. 45
(2012) 395203 (24pp
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