Brown-Henneaux's Canonical Approach to Topologically Massive Gravity

TL;DR

This paper applies the canonical approach to topologically massive gravity with a Chern-Simons term, confirming the boundary conformal symmetry with asymmetric central charges and relating black hole entropy to Wald's formula.

Contribution

It extends Brown-Henneaux's canonical analysis to include the gravitational Chern-Simons term, revealing asymmetric central charges and consistency with entropy formulas.

Findings

Boundary theory exhibits conformal symmetry with Virasoro algebras.

Central charges are asymmetric due to the Chern-Simons term.

Cardy's formula matches the extended Wald entropy for BTZ black holes.

Abstract

We analyze the symmetry realized asymptotically on the two dimensional boundary of AdS_3 geometry in topologically massive gravity, which consists of the gravitational Chern-Simons term as well as the usual Einstein-Hilbert and negative cosmological constant terms. Our analysis is based on the conventional canonical method and proceeds along the line completely parallel to the original Brown and Henneaux's. In spite of the presence of the gravitational Chern-Simons term, it is confirmed by the canonical method that the boundary theory actually has the conformal symmetry satisfying the left and right moving Virasoro algebras. The central charges of the Virasoro algebras are computed explicitly and are shown to be left-right asymmetric due to the gravitational Chern-Simons term. It is also argued that the Cardy's formula for the BTZ black hole entropy capturing all higher derivative corrections agrees with the extended version of the Wald's entropy formula. The M5-brane system is illustrated as an application of the present calculation.