Chiral and Real N=2 supersymmetric l-conformal Galilei algebras

TL;DR

This paper constructs and analyzes two types of N=2 supersymmetric extensions of the l-conformal Galilei algebra, introducing a new superalgebra and exploring its representations and central extensions.

Contribution

It introduces a new chiral N=2 superalgebra, compares it with the real case, and studies their representations and possible central extensions.

Findings

The chiral N=2 superalgebra is a new mathematical structure.

Both superalgebras admit finite truncations for integer and half-integer l.

The new superalgebra admits two types of central extensions depending on dimension and l.

Abstract

Inequivalent N=2 supersymmetrizations of the l-conformal Galilei algebra in d-spatial dimensions are constructed from the chiral (2,2) and the real (1,2,1) basic supermultiplets of the N=2 supersymmetry. For non-negative integer and half-integer l both superalgebras admit a consistent truncation with a (different) finite number of generators. The real N=2 case coincides with the superalgebra introduced by Masterov, while the chiral N=2 case is a new superalgebra. We present D-module representations of both superalgebras. Then we investigate the new superalgebra derived from the chiral supermultiplet. It is shown that it admits two types of central extensions, one is found for any d and half-integer l and the other only for d=2 and integer l. For each central extension the centrally extended l-superconformal Galilei algebra is realized in terms of its super-Heisenberg subalgebra generators.