6,893 research outputs found
Regularization of odd-dimensional AdS gravity: Kounterterms
As an alternative to the Dirichlet counterterms prescription, I introduce the
concept of Kounterterms as the boundary terms with explicit dependence on the
extrinsic curvature K_{ij} that regularize the AdS gravity action. Instead of a
Dirichlet boundary condition on the metric, a suitable choice of the boundary
conditions --compatible with any asymptotically AdS (AAdS) spacetime-- ensures
a finite action principle for all odd dimensions. Background-independent
conserved quantities are obtained as Noether charges associated to asymptotic
symmetries and their general expression appears naturally split in two parts.
The first one gives the correct mass and angular momentum for AAdS black
holes and vanishes identically for globally AdS spacetimes. Thus, the second
part is a covariant formula for the vacuum energy in AAdS spacetimes and
reproduces the results obtained by the Dirichlet counterterms method in a
number of cases. It is also shown that this Kounterterms series regularizes the
Euclidean action and recovers the correct black hole thermodynamics in odd
dimensions.Comment: 35+6 pages, 8 references and an appendix added, improved discussion
on boundary conditions and geometrical origin of Kounterterms. Version
accepted in JHE
Paperclip at
We study the ``paperclip'' model of boundary interaction with the topological
angle equal to . We propose exact expression for the disk
partition function in terms of solutions of certain ordinary differential
equation. Large distance asymptotic form of the partition function which
follows from this proposal makes it possible to identify the infrared fixed
point of the paperclip boundary flow at .Comment: 22 pages, 4 figure
From rubber bands to rational maps: A research report
This research report outlines work, partially joint with Jeremy Kahn and
Kevin Pilgrim, which gives parallel theories of elastic graphs and conformal
surfaces with boundary. One one hand, this lets us tell when one rubber band
network is looser than another, and on the other hand tell when one conformal
surface embeds in another.
We apply this to give a new characterization of hyperbolic critically finite
rational maps among branched self-coverings of the sphere, by a positive
criterion: a branched covering is equivalent to a hyperbolic rational map if
and only if there is an elastic graph with a particular "self-embedding"
property. This complements the earlier negative criterion of W. Thurston.Comment: 52 pages, numerous figures. v2: New example
Topological regularization and self-duality in four-dimensional anti-de Sitter gravity
It is shown that the addition of a topological invariant (Gauss-Bonnet term)
to the anti-de Sitter (AdS) gravity action in four dimensions recovers the
standard regularization given by holographic renormalization procedure. This
crucial step makes possible the inclusion of an odd parity invariant
(Pontryagin term) whose coupling is fixed by demanding an asymptotic (anti)
self-dual condition on the Weyl tensor. This argument allows to find the dual
point of the theory where the holographic stress tensor is related to the
boundary Cotton tensor as , which
has been observed in recent literature in solitonic solutions and hydrodynamic
models.
A general procedure to generate the counterterm series for AdS gravity in any
even dimension from the corresponding Euler term is also briefly discussed.Comment: 13 pages, no figures; enlarged discussion on self-duality condition
for AAdS spacetimes, references added, final version for PR
Lectures on quantization of gauge systems
A gauge system is a classical field theory where among the fields there are
connections in a principal G-bundle over the space-time manifold and the
classical action is either invariant or transforms appropriately with respect
to the action of the gauge group. The lectures are focused on the path integral
quantization of such systems. Here two main examples of gauge systems are
Yang-Mills and Chern-Simons.Comment: 63 pages, 22 figures. Based on lectures given at the Summer School
"New paths towards quantum gravity", Holbaek, Denmark, 200
Open strings, 2D gravity and AdS/CFT correspondence
We present a detailed discussion of the duality between dilaton gravity on
AdS_2 and open strings. The correspondence between the two theories is
established using their symmetries and field theoretical, thermodynamic, and
statistical arguments. We use the dual conformal field theory to describe
two-dimensional black holes. In particular, all the semiclassical features of
the black holes, including the entropy, have a natural interpretation in terms
of the dual microscopic conformal dynamics. The previous results are discussed
in the general framework of the Anti-de Sitter/Conformal Field Theory
dualities.Comment: 22 pages, Typeset using REVTE
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