New Chiral Gravity

TL;DR

This paper explores a new version of three-dimensional chiral gravity with specific boundary conditions, revealing special points where the symmetry algebra simplifies and black hole energies are positive, with implications for understanding black hole entropy.

Contribution

It identifies special points in topologically massive gravity where asymptotic symmetries simplify to chiral algebras, ensuring positive energy for black holes and excitations.

Findings

Asymptotic symmetry algebra includes Virasoro and Kač-Moody components.

At special coupling points, symmetries reduce to chiral Virasoro or Kač-Moody.

Black hole and excitation energies are positive at these points.

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 $\hat{u}(1)$ Ka\v{c}-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 $\mu = \pm {1\over \ell}$, the asymptotic symmetries reduce to either a chiral Virasoro algebra or a pure $\hat{u}(1)$ Ka\v{c}-Moody current algebra. At those points, black holes have positive energy while that of linearized excitations are non-negative.