Semi-classical central charge in topologically massive gravity

TL;DR

This paper addresses the holographic interpretation of spacelike warped $AdS_3$ geometries in Topologically Massive Gravity by deriving their asymptotic symmetry algebra using covariant phase-space methods. It identifies a two-component algebra consisting of a Virasoro part and a current algebra and computes the right-moving central charge $c_R = \frac{(5 {\hat{\nu}}^2+3)l}{G {\hat{\nu}}({\hat{\nu}}^2+3)}$, with a centrally extended current sector as well. It also shows that $L_0$ is bounded below for regular black holes with $G>0$, indicating a positive energy spectrum, and discusses the possibility of a Sugawara-type construction for a left-moving sector. The results bolster the conjectured dual CFT description of spacelike warped AdS backgrounds and clarify the impact of the gravitational Chern-Simons term on boundary charges.

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 $c_R = \frac{(5\hatν^2+3)l}{G\hatν (\hatν^2+3)}$ 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.