Supersymmetric Extension of Galilean Conformal Algebras

TL;DR

This paper extends the Galilean conformal algebra to include N=1 supersymmetry, resulting in a superalgebra that can be naturally extended to an infinite-dimensional structure, differing from the superconformal algebra in two dimensions.

Contribution

The paper constructs the N=1 Super Galilean conformal algebra via superspace coordinates and demonstrates its extension to an infinite algebra, providing a new supersymmetric non-relativistic symmetry framework.

Findings

Extended finite algebra to an infinite one

Constructed N=1 superalgebra in superspace

Identified structural differences from 2D superconformal algebra

Abstract

The Galilean conformal algebra has recently been realised in the study of the non-relativistic limit of the AdS/CFT conjecture. This was obtained by a systematic parametric group contraction of the parent relativistic conformal field theory. In this paper, we extend the analysis to include supersymmetry. We work at the level of the co-ordinates in superspace to construct the N=1 Super Galilean conformal algebra. One of the interesting outcomes of the analysis is that one is able to naturally extend the finite algebra to an infinite one. This looks structurally similar to the N=1 superconformal algebra in two dimensions, but is different. We also comment on the extension of our construction to cases of higher $N$.