Canonical structure of 3D gravity with torsion

TL;DR

This work analyzes the canonical structure of topological 3D gravity with torsion within the Mielke–Baekler Poincaré gauge formulation, focusing on AdS asymptotics. It demonstrates that the asymptotic symmetry algebra consists of two independent Virasoro algebras with classical central charges that generally differ, reflecting the influence of torsion (α3) on the boundary dynamics. The study provides explicit expressions for conserved charges of a Riemann–Cartan BTZ-like black hole and shows how torsion modifies energy and angular momentum relative to standard BTZ geometry. Overall, the results illuminate how torsion reshapes the canonical and asymptotic structure of 3D gravity and bears on potential quantum implications.

Abstract

We study the canonical structure of the topological 3D gravity with torsion, assuming the anti-de Sitter asymptotic conditions. It is shown that the Poisson bracket algebra of the canonical generators has the form of two independent Virasoro algebras with classical central charges. In contrast to the case of general relativity with a cosmological constant, the values of the central charges are different from each other.