Interacting SUSY-singlet matter in non-relativistic Chern-Simons theory

TL;DR

This paper constructs a non-relativistic supersymmetric Chern-Simons-matter theory with a singlet matter field, highlighting mismatched bosonic and fermionic degrees of freedom and analyzing the index for this mismatch.

Contribution

It introduces a novel non-relativistic SUSY Chern-Simons-matter model with a singlet matter field and explores its unique degree-of-freedom mismatch.

Findings

Bosonic and fermionic degrees of freedom do not match in the constructed theory.

The index analysis reveals the nature of the degree-of-freedom mismatch.

The model is derived as a non-relativistic limit of an N=2 theory.

Abstract

We construct an example of supersymmetric Chern-Simons-matter theory with a matter field transforming as a singlet representation of the supersymmetry algebra, where the bosonic and fermionic degrees of freedom do not match. This is obtained as a non-relativistic limit of the N=2 Chern-Simons-matter theory in 1+2 dimensions, where the particle and anti-particle coexist. We also study the index to investigate the mimatch of bosonic and fermionic degrees of freedom.