Chern-Simons formulation of three-dimensional gravity with torsion and nonmetricity
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.
Keywords
Cite
@article{arxiv.hep-th/0507200,
title = {Chern-Simons formulation of three-dimensional gravity with torsion and nonmetricity},
author = {Sergio L. Cacciatori and Marco M. Caldarelli and Alex Giacomini and Dietmar Klemm and Diego S. Mansi},
journal= {arXiv preprint arXiv:hep-th/0507200},
year = {2009}
}
Comments
24 pages, uses JHEP3.cls. Published version