Addition of torsion to chiral gravity

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 the Chern-Simons theory, where one of the two coupling constants of the $SL(2,\mathbb{R})$ actions vanishes. A prescription to approach this point in the space of parameters is discussed, and the canonical structure of the theory is analyzed.