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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Coussaert et al. (1995) studied this question.
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