N=1,2,3 l-conformal Galilei superalgebras

TL;DR

This paper constructs new N=1,2,3 supersymmetric extensions of the l-conformal Galilei algebra, providing explicit realizations and expanding the algebraic structures in supersymmetric nonrelativistic theories.

Contribution

It introduces novel N=1,2,3 l-conformal Galilei superalgebras and their differential operator realizations, extending previous algebraic frameworks.

Findings

New N=1,2,3 superalgebras constructed

Differential operator realizations provided

Extensions follow from supermultiplet analogy

Abstract

The issue of constructing N=1,2,3 supersymmetric extensions of the l-conformal Galilei algebra is reconsidered following the approach in [JHEP 1709 (2017) 131]. Drawing a parallel between acceleration generators entering the superalgebra and irreducible supermultiplets of d=1, N-extended superconformal group, a new N=1 l-conformal Galilei superalgebra, two new N=2 variants, and two new N=3 versions are built. Realisations in terms of differential operators in superspace are given.