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

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) and 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 and negative effective cosmological constant respectively. Choosing SO(3, 2) as the 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. (c) 2006 Elsevier B.V. All rights reserved.