On Holomorphic Factorization in Asymptotically AdS 3D Gravity
Abstract
This paper studies aspects of ``holography'' for Euclidean signature pure gravity on asymptotically AdS 3-manifolds. This theory can be described as SL(2,C) CS theory. However, not all configurations of CS theory correspond to asymptotically AdS 3-manifolds. We show that configurations that do have the metric interpretation are parameterized by the so-called projective structures on the boundary. The corresponding asymptotic phase space is shown to be the cotangent bundle over the Schottky space of the boundary. This singles out a ``gravitational'' sector of the SL(2,C) CS theory. It is over this sector that the path integral has to be taken to obtain the gravity partition function. We sketch an argument for holomorphic factorization of this partition function.
Keywords
Cite
@article{arxiv.hep-th/0109198,
title = {On Holomorphic Factorization in Asymptotically AdS 3D Gravity},
author = {Kirill Krasnov},
journal= {arXiv preprint arXiv:hep-th/0109198},
year = {2009}
}
Comments
32+1 pages, no figures; (v2) one reference added, a statement regarding priorities modified; (v3) presentational changes, an important sign mistake corrected