3D gravity with torsion as a Chern-Simons gauge theory

TL;DR

This paper demonstrates that topological 3D gravity with torsion can be reformulated as a Chern-Simons gauge theory when the effective cosmological constant is negative, linking it to boundary conformal field theories with two central charges.

Contribution

It establishes a novel formulation of 3D gravity with torsion as a Chern-Simons gauge theory under specific conditions, expanding the understanding of its boundary dynamics.

Findings

Gravity with torsion is equivalent to a Chern-Simons gauge theory.

Boundary dynamics correspond to a conformal field theory with two central charges.

Effective cosmological constant must be negative for this formulation.

Abstract

We show that topological 3D gravity with torsion can be formulated as a Chern-Simons gauge theory, provided a specific parameter, known as the effective cosmological constant, is negative. In that case, the boundary dynamics of the theory corresponding to anti-de Sitter boundary conditions is described by a conformal field theory with two different central charges.