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

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 $SL(2,R)\times SL(2,R)$ 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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• The Black Hole in Three Dimensional Space Time
• Geometry of the 2+1 Black Hole
• The Statistical Mechanics of the (2+1)-Dimensional Black Hole
• Conformal Edge Currents in Chern-Simons Theories

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