Chiral Quartic Massive Gravity in Three Dimensions

TL;DR

This work extends 3D gravity with quartic higher-curvature terms to CSS boundary conditions, identifying a Warped-CFT dual via a semidirect Virasoro $\times$ $U(1)$ KM symmetry. Using covariant phase-space methods, it derives the charge algebra and expresses the KM level $k$ and right-moving central charge $c_R$ in terms of the couplings, then computes BTZ entropy from the warped Cardy formula and analyzes linearized gravitons in an $U(1)\times SL(2,R)_R$ framework. The main results show non-negative graviton energies at two chiral points and reproduce known limits (e.g., NMG, TMG) when parameters are specialized, highlighting the consistency of the CSS/WCFT correspondence in higher-curvature 3D gravity. These findings advance the understanding of holography for non-AdS boundary conditions and the stability/unitarity landscape of higher-derivative massive gravity in three dimensions.

Abstract

We study minimal massive gravity with cubic and quartic terms in Compere, Song, and Strominger (CSS) boundary conditions. By employing a semi-product of a Virasoro and a $U(1)$ Kac-Moody current algebra as the asymptotic symmetry algebra, we calculate the entropy of BTZ black holes via the degeneracy of states belonging to a Warped-CFT. Then, we compute the linearized energy excitations using the representations of the algebra $U(1)\times SL(2, R)_{R}$ and demonstrate that the energies of excitations are non-negative at two chiral points in the parameter space.