Chiral Gravity in Three Dimensions

TL;DR

This work analyzes three-dimensional gravity with negative cosmological constant deformed by a gravitational Chern-Simons term (TMG). It identifies a critical point, $\mu\ell=1$, where the theory becomes chiral, with a purely right-moving boundary sector and nonnegative BTZ and graviton energies under suitable boundary conditions, suggesting a unitary holographic dual and a microscopic entropy description via the Cardy formula. The paper derives the central charges and graviton spectra, shows how energies depend on $\mu$, and discusses the necessity of boundary conditions to render the left-moving sector pure gauge. While promising as a consistent quantum theory, it highlights open challenges in nonlinear positivity, renormalizability, and explicit construction of the dual CFT.

Abstract

Three dimensional Einstein gravity with negative cosmological constant -1/\ell^2 deformed by a gravitational Chern-Simons action with coefficient 1/μis studied in an asymptotically AdS_3 spacetime. It is argued to violate unitary or positivity for generic μdue to negative-energy massive gravitons. However at the critical value μ\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).