Chern--Simons formulation of three-dimensional gravity with torsion and nonmetricity (Q857407)

Various models of three-dimensional metric affine gravity are considered and it is shown that they can be written as Chern-Simons theories. Starting from the usual formulation of three-dimensional gravity and using a nonstandard decomposition of the Chern-Simons connection, the Mielke-Baekler model for arbitrary sign of the effective cosmological constant is recovered. The three-dimensional gravity with torsion is realized as a Chern-Simons theory. Torsionless but nonmetric gravitational models are considered as well.