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29 March 2024
 
  » arxiv » hep-th/0109198

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On Holomorphic Factorization in Asymptotically AdS 3D Gravity
Kirill Krasnov ;
Date 25 Sep 2001
Journal Class.Quant.Grav. 20 (2003) 4015-4042
Subject hep-th gr-qc
AffiliationAEI
AbstractThis 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.
Source arXiv, hep-th/0109198
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