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

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.