Anti-de Sitter 3-dimensional Gravity with Torsion

TL;DR

This paper investigates the asymptotic symmetries of 3D gravity with torsion in anti-de Sitter space, revealing two Virasoro algebras with classical central charges and analyzing their differences in various geometries.

Contribution

It provides a canonical analysis of the asymptotic symmetries in 3D gravity with torsion, highlighting the structure of Virasoro algebras and their central charges.

Findings

Two independent Virasoro algebras with classical central charges.

Equal central charges in teleparallel vacuum geometry.

Different central charges in Riemann-Cartan geometry.

Abstract

Using the canonical formalism, we study the asymptotic symmetries of the topological 3-dimensional gravity with torsion. In the anti-de Sitter sector, the symmetries are realized by two independent Virasoro algebras with classical central charges. In the simple case of the teleparallel vacuum geometry, the central charges are equal to each other and have the same value as in general relativity, while in the general Riemann-Cartan geometry, they become different.