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Chern–Simons formulation of three-dimensional gravity with torsion and nonmetricity. (English) Zbl 1109.83007
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.

83D05 Relativistic gravitational theories other than Einstein’s, including asymmetric field theories
83C80 Analogues of general relativity in lower dimensions
83C45 Quantization of the gravitational field
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