Non-relativistic three-dimensional supergravity theories and semigroup expansion method

TL;DR

This paper introduces a systematic semigroup expansion method to construct diverse non-relativistic supergravity theories in three dimensions, providing new models and insights into their algebraic structures and relations.

Contribution

It applies the Lie algebra expansion method to supersymmetric algebras, generating new non-relativistic supergravity models and their invariant tensors systematically.

Findings

Derived new non-relativistic superalgebras from supersymmetric extensions.

Constructed invariant tensors for expanded superalgebras.

Showed relationships between different supergravity models via contractions.

Abstract

In this work we present an alternative method to construct diverse non-relativistic Chern-Simons supergravity theories in three spacetime dimensions. To this end, we apply the Lie algebra expansion method based on semigroups to a supersymmetric extension of the Nappi-Witten algebra. Two different families of non-relativistic superalgebras are obtained, corresponding to generalizations of the extended Bargmann superalgebra and extended Newton-Hooke superalgebra, respectively. The expansion method considered here allows to obtain known and new non-relativistic supergravity models in a systematic way. In particular, it immediately provides an invariant tensor for the expanded superalgebra, which is essential to construct the corresponding Chern-Simons supergravity action. We show that the extended Bargmann supergravity and its Maxwellian generalization appear as particular subcases of a generalized extended Bargmann supergravity theory. In addition, we demonstrate that the generalized extended Bargmann and generalized extended Newton-Hooke supergravity families are related through a contraction process.