New Chiral Gravity

TL;DR

This work analyzes Compere-Song-Strominger CSS boundary conditions for $AdS_3$ gravity and their embedding into Topologically Massive Gravity (TMG). By computing modified Virasoro-Kac-Moody charges in TMG, it identifies two special coupling points, $\mu\ell = \pm 1$, where the asymptotic symmetry algebra truncates to a chiral Virasoro (for $\mu\ell=1$) or a pure $\hat{u}(1)$ Kač-Moody (for $\mu\ell=-1$); in both cases BTZ black holes retain positive energy and their entropy is reproduced by Warped CFT Cardy formulas. The work provides explicit expressions for the tilde charges and central extensions, analyzes black hole thermodynamics, and classifies linearized gravitons under the CSS boundary conditions, revealing stable, unitary-like behavior at the special points. The results point toward dual descriptions in terms of holomorphic CFTs or WCFTs and open avenues for generalizations to logarithmic WCFTs and non-Einstein solutions, with potential implications for holography in warped/adS contexts.

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 $μ$. When $μ= \pm {1\over \ell}$, 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.