Semi-classical central charge in topologically massive gravity

TL;DR

This paper analyzes the asymptotic symmetries of warped black hole geometries in topologically massive gravity, deriving the central charges of the associated Virasoro and current algebras, which are crucial for understanding their holographic duals.

Contribution

It demonstrates that warped black holes admit an algebra of asymptotic symmetries combining Virasoro and current algebras, and computes their central charges.

Findings

Right-moving central charge $c_R$ explicitly derived.

Asymptotic symmetry algebra is a semi-direct product of Virasoro and current algebra.

Current algebra is shown to be centrally extended.

Abstract

It is shown that the warped black holes geometries discussed recently in 0807.3040 admit an algebra of asymptotic symmetries isomorphic to the semi-direct product of a Virasoro algebra and an algebra of currents. The realization of this asymptotic symmetry by canonical charges allows one to find the central charge of the Virasoro algebra. The right-moving central charge $c_R = \frac{(5\hat{\nu}^2+3)l}{G\hat{\nu} (\hat{\nu}^2+3)}$ is obtained when the Virasoro generators are normalized in order to have a positive zero mode spectrum for the warped black holes. The current algebra is also shown to be centrally-extended.