Chern–Simons formulation of three-dimensional gravity with torsion and nonmetricity |
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Authors: | Sergio L Cacciatori Marco M Caldarelli Alex Giacomini Dietmar Klemm Diego S Mansi |
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Institution: | aDipartimento di Matematica dell’Università di Milano, Via Saldini 50, I-20133 Milano, Italy bDipartimento di Fisica dell’Università di Milano, Via Celoria 16, I-20133 Milano, Italy cINFN, Sezione di Milano, Via Celoria 16, I-20133 Milano, Italy |
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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 , and , 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 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 Chern–Simons theory. |
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Keywords: | Chern–Simons theories Models of quantum gravity Differential geometry |
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