Dynamics of Asymptotic Diffeomorphisms in (2+1)-Dimensional Gravity

TL;DR

This paper demonstrates that in (2+1)-dimensional asymptotically anti-de Sitter gravity, boundary-changing diffeomorphisms are governed by a Liouville action, capturing the black hole entropy through their dynamics.

Contribution

It establishes that the boundary degrees of freedom in 2+1D AdS gravity are described by a Liouville theory with the correct central charge for BTZ black hole entropy.

Findings

Boundary diffeomorphisms are physical degrees of freedom.

Liouville action accurately models these boundary dynamics.

Reproduces BTZ black hole entropy from boundary theory.

Abstract

In asymptotically anti-de Sitter gravity, diffeomorphisms that change the conformal boundary data can be promoted to genuine physical degrees of freedom. I show that in 2+1 dimensions, the dynamics of these degrees of freedom is described by a Liouville action, with the correct central charge to reproduce the entropy of the BTZ black hole.