N = 2 Galilean superconformal algebras with central extension

TL;DR

This paper explores N=2 supersymmetric extensions of the Galilean conformal algebra, revealing new types of central extensions and providing realizations for both standard and exotic super-GCAs, along with an N=1 extension.

Contribution

It introduces a novel super-GCA for arbitrary , identifying new central extensions and realizations, expanding the understanding of supersymmetric Galilean conformal algebras.

Findings

Identified two types of central extensions depending on parity of 2.

Constructed a super-GCA corresponding to the exotic extension.

Provided realizations of standard and exotic super-GCAs.

Abstract

N = 2 Supersymmetric extensions of Galilean conformal algebra (GCA), specified by spin \ell and dimension of space d, are investigated. Duval and Horvathy showed that the \ell = 1/2 GCA has two types of supersymmetric extensions, called standard and exotic. Recently, Masterov intorduced a centerless super-GCA for arbitrary \ell wchich corresponds to the standard extension. We show that the Masterov's super-GCA has two types of central extensions depending on the parity of 2\ell. We then introduced a novel super-GCA for arbitrary \ell corresponding to the exotic extension. It is shown that the exotic superalgebra also has two types of central extensions depending on the parity of 2\ell. Furthermore, we give a realization of the standard and exotic super-GCA's in terms of their subalgebras. Finally, we present a N = 1 supersmmetric extension of GCA with central extensions.