On Holomorphic Factorization in Asymptotically AdS 3D Gravity

Details On Holomorphic Factorization in Asymptotically AdS 3D Gravity On Holomorphic Factorization in Asymptotically AdS 3D Gravity

2001-09-25

arxiv.org/abs/hep-th/0109198v3

Class.Quant.Grav. 20 (2003) 4015-4042

Physics

High Energy Physics

High Energy Physics - Theory

32+1 pages, no figures; (v2) one reference added, a statement regarding priorities modified; (v3) presentational changes, an i

Scientific paper

10.1088/0264-9381/20/18/311

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.

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