Supersymmetric Extension of GCA in 2d

TL;DR

This paper derives the infinite-dimensional Supersymmetric Galilean Conformal Algebra (SGCA) in 2d via group contraction of superconformal algebra, explores its representations, and connects it to non-unitary 2d SCFTs with large, opposite central charges.

Contribution

It introduces the supersymmetric extension of the 2d GCA, providing new algebraic structures, representations, and correlation function insights in a non-unitary context.

Findings

Derived the 2d SGCA through group contraction.

Constructed representations using superspace coordinates.

Analyzed correlation functions and null states in the SGCA.

Abstract

We derive the infinite dimensional Supersymmetric Galilean Conformal Algebra (SGCA) in the case of two spacetime dimensions by performing group contraction on 2d superconformal algebra. We also obtain the representations of the generators in terms of superspace coordinates. Here we find realisations of the SGCA by considering scaling limits of certain 2d SCFTs which are non-unitary and have their left and right central charges become large in magnitude and opposite in sign. We focus on the Neveu-Schwarz sector of the parent SCFTs and develop, in parallel to the GCA studies recently in (arXiv:0912.1090), the representation theory based on SGCA primaries, Ward identities for their correlation functions and their descendants which are null states.