Generalised Bargmann Superalgebras

TL;DR

This paper classifies N=1 and N=2 super-extensions of non-relativistic symmetry algebras in 3+1 dimensions, providing a foundation for potential applications in non-relativistic supergravity and holography.

Contribution

It systematically classifies super-extensions of Bargmann and related algebras, identifying 9 N=1 and 22 N=2 classes, a novel comprehensive algebraic analysis.

Findings

9 isomorphism classes of N=1 superalgebras

22 branches of N=2 superalgebras

Potential applications in non-relativistic supergravity and holography

Abstract

The Bargmann algebra and centrally-extended Newton-Hooke algebras describe the non-relativistic symmetries of massive particles in flat and curved spacetimes, respectively. These three algebras all arise as deformations of the universal central-extension of the static kinematical Lie algebra. In this paper, we classify the N=1 super-extensions for each of these algebras in (3+1)-dimensions, up to isomorphism. We then identify the non-empty branches of the algebraic variety describing the N=2 super-extensions of these algebras. We find 9 isomorphism classes in the N=1 case and 22 branches in the N=2 case. We then give a brief discussion on some applications of these Lie superalgebras, including their possible uses for non-relativistic supergravity and holography.