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 $SL(2,R) \times SL(2,R)$ 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.Comment: 10 pages in LaTeX, LaTeX problem fixe

Driel, “The Asymptotic dynamics of three-dimensional Einstein gravity with a negative cosmological constant,” Class.Quant.Grav

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 spacetime 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