Supersymmetric Extension of Galilean Conformal Algebras

TL;DR

This work derives a non-relativistic contraction of the ${\mathcal{N}}=1$ superconformal algebra to construct the ${\mathcal{N}}=1$ Super Galilean Conformal Algebra (SGCA) in superspace. The finite SGCA combines bosonic and fermionic generators with a $U(1)$ R-symmetry, and remarkably admits an infinite-dimensional extension analogous to Virasoro and current algebras, though with distinctive fermionic structure that yields a cousin of the 2D superconformal algebra. The authors present a detailed infinite lift with mode generators $L_n$, $M_n^i$, $A_n$, and $G_r^{\pm a}$, including the action of ${\mathcal{A}}_n$ and the impossibility of lifting $J^i$ to an infinite current. They also discuss generalizations to higher ${\mathcal{N}}$, emphasizing the absence of central terms in the fermionic sectors and the enhanced R-symmetry, and outline potential applications to non-relativistic sectors of ${\mathcal{N}}=4$ SYM and the corresponding AdS/CFT duals. Altogether, the paper provides a systematic framework for supersymmetric and infinite extensions of Galilean conformal symmetries with implications for non-relativistic holography.

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 $N$.