Super-GCA from $\mathcal{N} = (2,2)$ Super-Virasoro

TL;DR

This paper derives the extended supersymmetric Galilean conformal algebra in two dimensions from the super-Virasoro algebra using group contraction, and explores its representation theory and correlation functions.

Contribution

It introduces the extended 2D supersymmetric Galilean conformal algebra via contraction of super-Virasoro algebra, including its representation theory and superspace formalism.

Findings

Derived the extended SGCA from super-Virasoro algebra.

Developed the representation theory of the algebra.

Analyzed correlation functions and supermultiplets.

Abstract

We derive the extended Supersymmetric Galilean Conformal Algebra (SGCA) in two spacetime dimensions by the method of group contraction on $2d$ $\mathcal{N}=(2,2)$ superconformal algebra. Both the parent and daughter algebras are infinite-dimensional. We provide the representation theory of the algebra. We adopt a superspace formalism for the SGCA fields, allowing us to write them down in a compact notation as components of superfields. We also discuss correlation functions, short supermultiplets and null states.