Chern-Simons formulation of three-dimensional gravity with torsion and nonmetricity

TL;DR

This paper demonstrates that various three-dimensional gravity models with torsion and nonmetricity can be formulated as Chern-Simons theories with different gauge groups, unifying diverse gravity theories in a topological framework.

Contribution

It introduces a unified Chern-Simons formulation for 3D gravity models with torsion and nonmetricity, including new models based on SL(4,R).

Findings

Reformulation of Mielke-Baekler model as Chern-Simons theory.

Generalization of conformal gravity with Weyl structure.

Introduction of a novel topological metric affine gravity model.

Abstract

We consider various models of three-dimensional gravity with torsion or nonmetricity (metric affine gravity), and show that they can be written as Chern-Simons theories with suitable gauge groups. Using the groups ISO(2,1), SL(2,C) or SL(2,R) x SL(2,R), and the fact that they admit two independent coupling constants, we obtain the Mielke-Baekler model for zero, positive or negative effective cosmological constant respectively. Choosing SO(3,2) as gauge group, one gets a generalization of conformal gravity that has zero torsion and only the trace part of the nonmetricity. This characterizes a Weyl structure. Finally, we present a new topological model of metric affine gravity in three dimensions arising from an SL(4,R) Chern-Simons theory.