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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.

##### MSC:
 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
##### Keywords:
Chern-Simons theories; torsion; nonmetricity
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##### References:
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