Lie Algebra Expansions, Non-Relativistic Matter Multiplets and Actions

TL;DR

This paper introduces a Lie algebra expansion method to construct off-shell matter multiplets and actions for non-relativistic superalgebras, extending previous on-shell supergravity models to off-shell frameworks.

Contribution

It develops a systematic approach using Lie algebra expansion to generate off-shell matter multiplets and actions for non-relativistic superalgebras, with explicit examples in 3D and 4D.

Findings

Constructed off-shell multiplets for non-relativistic superalgebras.

Provided explicit transformation rules and actions in 3D and 4D.

Extended the Lie algebra expansion technique to off-shell matter theories.

Abstract

We discuss a general methodology to provide rigid, off-shell matter multiplets and actions for recently constructed non-relativistic superalgebras. The technique is based on the Lie algebra expansion, which, in the context of supersymmetry, has so far been used to obtain non-relativistic on-shell supergravity models. We first explain how the Lie algebra expansion can be implemented to generate off-shell rigid multiplets on a flat background by developing an auxiliary framework where only the lowest order behavior of the spatial and temporal vielbein is relevant. We then provide explicit examples for the field content, the transformation rules as well as action principles for certain multiplets in three and four dimensions.