Abstract
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 {mathcal {N}}=2 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.
Highlights
Theory using the Chern–Simons (CS) formalism and considering the so-called teleparallel algebra [17]
In this work we have presented the NR counterpart of the teleparallel CSgravity theory in three spacetime dimensions
With involves additional Abelian generators, is required firstly to ensure a non-degenerate invariant tensor in the limit process to the NR theory and secondly to have a well-defined flat limit leading to the extended Bargmann symmetry
Summary
Non-relativistic (NR) theories have received a growing interest due to their relation to condensed matter systems [19–30] and NR effective field theories [31– 35]. We are interested in studying the role of a nonvanishing torsion in a non-relativistic environment To this end, we first explore the NR limit of a particular U (1)enlargement of the teleparallel algebra introduced in [17]. The supersymmetric extension of our theory is presented by applying the S-expansion to the N = 2 teleparallel superalgebra presented in [17] As it was shown in [64,65], a particular semigroup allows to reproduce a Galilean expansion providing the respective NR (super)algebra and (super)gravity CS action. The novel torsional NR (super)gravity theory and the extended Bargmann (super)gravity theory [54] are related through a vanishing cosmological constant limit as their respective relativistic versions.
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