New Chiral Gravity

Abstract

The phase space of three-dimensional gravity with Compere-Song-Strominger (CSS) boundary conditions is endowed with asymptotic symmetries consisting in the semi-direct product of a Virasoro and a $\hat{u}(1)$ Kač-Moody algebra, and contains BTZ black holes whose entropy can be accounted for by the degeneracy of states of a Warped CFT. By embedding these boundary conditions in Topologically Massive Gravity, we observe the existence of two special points in the space of couplings parameterized by the AdS${}_3$ radius $\ell$ and the Chern-Simons coupling $\mu$. When $\mu =\pm \frac{1}{\ell }$, the asymptotic symmetries reduce to either a chiral Virasoro algebra or a pure $\hat{u}(1)$ Kač-Moody current algebra. At those points, black holes have positive energy while that of linearized excitations are non-negative.

arXiv comment8 pages, latex, V3, minor modifications

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• Boundary Conditions for Warped AdS${}_3$ in Quadratic Ensemble