Supersymmetric Extension of GCA in 2d

TL;DR

The paper constructs the infinite dimensional 2d SGCA by contracting two copies of the 2d SuperVirasoro algebra and analyzes its representations, Ward identities, and null states in the NS sector. It develops primary and descendant structures, derives explicit transformation laws on a nonrelativistic superspace, and computes SGCA two-point and higher-point functions, including a nonrelativistic limit of 2d SCFT correlators. It further investigates level 3/2 null vectors, derives corresponding differential equations for SGCA correlators, and establishes fusion rules that mirror even-sector SCFT fusion in the SGCA limit. The work highlights the nonunitary nature of the SGCA, extra nonrelativistic null states not inherited from SCFT, and lays out open directions such as the Ramond sector and extensions to more supersymmetries.

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.