On the addition of torsion to chiral gravity

TL;DR

This paper explores three-dimensional Anti-de Sitter gravity with torsion, analyzing its algebraic structure, central charges, and special points where one charge vanishes, drawing parallels with chiral and topologically massive gravity.

Contribution

It reviews the derivation of central charges in AdS gravity with torsion and examines a special singular point related to chiral gravity, providing a new perspective on the theory's canonical structure.

Findings

Identification of a special point where one central charge vanishes

Comparison with chiral point of topologically massive gravity

Analysis of the canonical structure at the singular point

Abstract

Three-dimensional gravity in Anti-de Sitter space is considered, including torsion. The derivation of the central charges of the algebra that generates the asymptotic isometry group of the theory is reviewed, and a special point of the theory, at which one of the central charges vanishes, is compared with the chiral point of topologically massive gravity. This special point corresponds to a singular point in Chern-Simons theory, where one of the two coupling constants of the SL(2,R) actions vanishes. A prescription to approach this point in the space of parameters is discussed, and the canonical structure of the theory is analyzed.