Chiral gravity in three dimensions

Abstract

Three dimensional Einstein gravity with negative cosmological constant -1/ℓ 2 deformed by a gravitational Chern-Simons action with coefficient 1/μ is studied in an asymptotically AdS 3 spacetime. It is argued to violate unitary or positivity for generic μ due to negative-energy massive gravitons. However at the critical value μℓ = 1, the massive gravitons disappear and BTZ black holes all have mass and angular momentum related by ℓM = 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) = (0,3ℓ/G).