Three-dimensional non-relativistic Hietarinta supergravity

TL;DR

This paper develops a non-relativistic version of Hietarinta supergravity using contraction and algebra expansion methods, revealing new structures and relations to extended Bargmann supergravity, with implications for torsion and cosmological constants.

Contribution

It introduces the non-relativistic Hietarinta supergravity via contraction and algebra expansion, extending previous models and including a cosmological constant.

Findings

Non-relativistic Hietarinta supergravity derived from contraction.

Relation to extended Bargmann supergravity established.

Effects of cosmological constant on torsion analyzed.

Abstract

In this work we present the non-relativistic regime of the Hietarinta gravity theory and its extension to supergravity. At the bosonic level, we derive the non-relativistic version of the Hietarinta model by employing a contraction process and addressing the non-degeneracy of the invariant metric. To incorporate supersymmetry, we apply the Lie algebra expansion method to obtain the non-relativistic formulation of $\mathcal{N}=2$ Hietarinta supergravity. Our results reveal that the non-relativistic Hietarinta theory encompasses the extended Bargmann (super)gravity as a special case, yet it differs significantly from other existing non-relativistic (super)gravity models. Furthermore, we generalize our analysis to include a cosmological constant term in the non-relativistic Hietarinta (super)gravity action and examine its effects on the torsion structure.