New Chiral Generalized Minimal Massive Gravity

TL;DR

This paper explores the properties of generalized minimal massive gravity (GMMG) with specific boundary conditions, analyzing black hole entropy, energy excitations, and algebraic structures at special parameter points, connecting to known 3D gravity models.

Contribution

It introduces a chiral extension of GMMG, analyzes its asymptotic symmetries, and links it to warped CFTs and known massive gravity theories in 2+1 dimensions.

Findings

BTZ black hole entropy matches warped-CFT degeneracy

Energy excitations are non-negative at chiral points

Charge algebra simplifies to Virasoro or Kac-Moody at special parameters

Abstract

We study the generalized minimal massive gravity (GMMG) in Compere, Song and Strominger boundary conditions employing a semi-product of a Virasoro and a $\hat{u}(1)$ Kac-Moody current algebras as the asymptotic symmetry algebra. We calculate the entropy of BTZ black holes via the degeneracy of states belonging to a Warped-CFT. We compute the linearized energy excitations by using the representations of the algebra $\hat{u}(1) \times SL(2,R)_R$ and show that energies of excitations are non-negative at (two) chiral points in the parameter space. At these special points, the charge algebra is described by either Virasoro algebra or Kac-Moody algebra. We also consider some special limits of the GMMG theory which correspond to $2+1$-dimensional massive gravity theories such as new massive and minimal massive gravity theories.