Chiral Gravity in Three Dimensions

Abstract

Three dimensional Einstein gravity with negative cosmological constant \(-1/\ell^2\) deformed by a gravitational Chern-Simons action with coefficient \(1/\mu\) is studied in an asymptotically \(AdS_3\) spacetime. It is argued to violate unitary or positivity for generic \(\mu\) due to negative-energy massive gravitons. However at the critical value \(\mu\ell=1\), the massive gravitons disappear and BTZ black holes all have mass and angular momentum related by \(\ell M=J\). The corresponding chiral quantum theory of gravity is conjectured to exist and be dual to a purely right-moving boundary CFT with central charges \((c_L,c_R)=(0,3\ell /G)\).