Supersymmetry and Bosonization in Three Dimensions

TL;DR

This paper explores the potential for supersymmetric invariance in three-dimensional fermionic systems and its connection to fermion-boson duality, demonstrating conditions under which supersymmetry emerges in low-energy regimes.

Contribution

It introduces a supersymmetric-like invariance in fermionic models and constructs the associated supercurrent and transformation laws in three dimensions.

Findings

Supersymmetry appears under specific mass conditions.

Supercurrent and transformation laws are explicitly constructed.

Supersymmetry is absent in the massless limit.

Abstract

We discuss on the possible existence of a supersymmetric invariance in purely fermionic planar systems and its relation to the fermion-boson mapping in three-dimensional quantum field theory. We consider, as a very simple example, the bosonization of free massive fermions and show that, under certain conditions on the masses, this model displays a supersymmetric-like invariance in the low energy regime. We construct the purely fermionic expression for the supercurrent and the non-linear supersymmetry transformation laws. We argue that the supersymmetry is absent in the limit of massless fermions where the bosonized theory is non-local.