From N=1 to N=2 supersymmetries in 2+1 dimensions

TL;DR

This paper constructs N=2 supersymmetric models in 2+1 dimensions from N=1 supermultiplets, including the Abelian-Higgs and pure super Yang-Mills models, confirming previous findings on supersymmetry enhancement.

Contribution

It provides a systematic method to derive N=2 supersymmetric theories in 2+1 dimensions starting from N=1 supermultiplets, extending the understanding of supersymmetry elevation.

Findings

Successfully constructs N=2 supersymmetric Abelian-Higgs model.

Derives N=2 pure super Yang-Mills model.

Confirms conditions for supersymmetry enhancement align with previous research.

Abstract

Starting from N=1 scalar and vector supermultiplets in 2+1 dimensions, we construct superfields which constitute Lagrangians invariant under N=2 supersymmetries. We first recover the N=2 supersymmetric Abelian-Higgs model and then the N=2 pure super Yang-Mills model. The conditions for this elevation are consistent with previous results found by other authors.