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

TL;DR

This paper demonstrates that the asymptotic behavior of 3D Einstein gravity with a negative cosmological constant can be described by Liouville theory, linking gravitational dynamics to a well-known conformal field theory.

Contribution

It establishes a connection between 3D Einstein gravity with negative cosmological constant and Liouville theory via Chern-Simons and WZW models, providing a new perspective on gravitational boundary dynamics.

Findings

Liouville theory describes the asymptotic dynamics of 3D Einstein gravity.

Chern-Simons theory with $SL(2,R) \times SL(2,R)$ is equivalent to a non-chiral $SL(2,R)$ WZW model.

Boundary conditions reduce the WZW model to Liouville theory.

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.