Extended Superconformal Galilean Symmetry in Chern-Simons Matter Systems

TL;DR

This paper explores the extended superconformal Galilean symmetry in nonrelativistic limits of N=2 supersymmetric Chern-Simons matter systems, revealing new symmetries, constraints on couplings, and implications for self-dual equations.

Contribution

It demonstrates the existence of extended superconformal Galilean symmetry in the model and shows how it constrains coupling constants to match known self-dual solutions.

Findings

Identification of extended superconformal Galilean symmetry.

Coupling constants fixed by symmetry to known self-dual values.

Analysis of the two-particle sector in the second quantized model.

Abstract

We study the nonrelativistic limit of the $N=2$ supersymmetric Chern-Simons matter system. We show that in addition to Galilean invariance the model admits a set of symmetries generated by fermionic charges, which can be interpreted as an {\it extended Galilean supersymmetry }. The system also possesses a hidden conformal invariance and then the full group of symmetries is the {\it extended superconformal Galilean} group. We also show that imposing extended superconformal Galilean symmetry determines the values of the coupling constants in such a way that their values in the bosonic sector agree with the values of Jackiw and Pi for which self-dual equation exist. We finally analyze the second quantized version of the model and the two-particle sector.