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The asymptotic dynamics of three-dimensional Einstein gravity with a negative cosmological constant

O. Coussaert, M. Henneaux, P. van Driel

gr-qcarXiv:gr-qc/9506019

Abstract

Liouville theory is shown to describe the asymptotic dynamics of three-dimensional Einstein gravity with a negative cosmological constant. This is because (i) Chern-Simons theory with a gauge group SL(2,R) × SL(2,R) on a space-time with a cylindrical boundary is equivalent to the non-chiral SL(2,R) WZW model; and (ii) the anti-de Sitter boundary conditions implement the constraints that reduce the WZW model to the Liouville theory.

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