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)xSL(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.

Chern-Simons formulation of three-dimensional gravity with torsion and nonmetricity / Sergio L. Cacciatori, Marco M. Caldarelli, Alex Giacomini, Dietmar Klemm, Diego S. Mansi. - In: JOURNAL OF GEOMETRY AND PHYSICS. - ISSN 0393-0440. - 56:12(2006), pp. 2523-2543. [10.1016/j.geomphys.2006.01.006]

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

Sergio L. Cacciatori;Marco M. Caldarelli;Dietmar Klemm;Diego S. Mansi
2006

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 ISO(2,1), SL(2,C) and SL(2,R)xSL(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.
Chern-Simons theories ; Models of quantum gravity ; Differential geometry
Settore FIS/02 - Fisica Teorica, Modelli e Metodi Matematici
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2434/25596
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