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

TL;DR

The paper demonstrates that the asymptotic dynamics of three-dimensional gravity with a negative cosmological constant are governed by Liouville theory. By recasting gravity as a Chern-Simons theory with gauge group SL(2,R) × SL(2,R) and applying AdS boundary conditions, the authors reduce the dynamics first to a non-chiral WZW model and then to Liouville theory via Hamiltonian reduction of currents. The resulting Liouville theory is conformally invariant and provides the Virasoro asymptotic generators for AdS3 gravity, clarifying the boundary CFT description. The work also outlines extensions to supersymmetry and energy positivity in future studies.

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.