Regular Article - Theoretical Physics
Three-dimensional non-relativistic supergravity and torsion
Departamento de Matemática y Física Aplicadas, Universidad Católica de la Santísima Concepción, Alonso de Ribera 2850, Concepción, Chile
2 DISAT, Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129, Turin, Italy
3 INFN, Sezione di Torino, Via P. Giuria 1, 10125, Turin, Italy
Accepted: 3 March 2022
Published online: 11 March 2022
In this paper we present a torsional non-relativi-stic Chern–Simons (super)gravity theory in three spacetime dimensions. We start by developing the non-relativistic limit of the purely bosonic relativistic teleparallel Chern–Simons formulation of gravity. On-shell the latter yields a non-Riemannian setup with non-vanishing torsion, which, at non-relativistic level, translates into a non-vanishing spatial torsion sourced by the cosmological constant. Then we consider the three-dimensional relativistic teleparallel Chern–Simons supergravity theory and obtain its non-relativistic counterpart by exploiting a Lie algebra expansion method. The non-relativistic supergravity theory is characterized, on-shell, by a non-vanishing spatial super-torsion, again sourced by the cosmological constant.
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