Vacua of Exotic Massive 3D Gravity

TL;DR

This paper explores the diverse vacuum solutions of exotic 3D massive gravity, revealing rich geometries including black holes and non-Einstein spaces, and suggests a duality with chiral conformal field theories.

Contribution

It identifies a variety of vacua in exotic 3D massive gravity, including non-Einstein geometries and black holes, and proposes a duality with chiral CFTs at specific parameter points.

Findings

Existence of asymptotically AdS geometries with different boundary conditions.

Presence of non-Einstein spaces with specific isometry groups.

Identification of black hole solutions with Log-gravity gravitons.

Abstract

We consider the recently proposed exotic 3D massive gravity. We show that this theory has a rich space of vacua, including asymptotically Anti de-Sitter (AdS) geometries obeying either the standard Brown-Henneaux boundary conditions or the weakened asymptotic behavior of the so-called Log-gravity. Both sectors contain non-Einstein spaces with $SO(2)\times \mathbb{R}$ isometry group, showing that the Birkhoff theorem does not hold all over the parameter space, even if strong AdS boundary conditions are imposed. Some of these geometries correspond to 3D black holes dressed with a Log-gravity graviton. We conjecture that such geometries appear in a curve of the parameter space where the exotic 3D massive gravity on AdS$_3$ is dual to a chiral conformal field theory. The theory also contains other interesting vacua, including different families of non-AdS black holes.