Three-dimensional non-relativistic supergravity and torsion

TL;DR

This paper develops a three-dimensional non-relativistic supergravity theory with torsion, derived from relativistic models via a Lie algebra expansion, revealing non-zero spatial torsion influenced by the cosmological constant.

Contribution

It introduces a novel non-relativistic supergravity framework with torsion, obtained through a systematic non-relativistic limit and algebra expansion of relativistic theories.

Findings

Non-relativistic limit of teleparallel Chern-Simons gravity yields non-zero torsion.

Non-relativistic supergravity characterized by spatial super-torsion sourced by cosmological constant.

Methodology bridges relativistic and non-relativistic supergravity theories.

Abstract

In this paper we present a torsional non-relativistic Chern-Simons teleparallel (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 $\mathcal{N}=2$ 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.