Connection between Space-Time Supersymmetry and Non-Commutative Geometry

TL;DR

This paper explores how extended supersymmetric Yang-Mills theories in four dimensions can be formulated as action functionals on non-commutative spaces, revealing a geometric perspective on supersymmetry.

Contribution

It demonstrates the derivation of N=2 and N=4 supersymmetric Yang-Mills theories as non-commutative geometric action functionals, and discusses restrictions for matter coupling.

Findings

N=2 and N=4 supersymmetric theories derived from non-commutative geometry

Matter coupling limited to models without a general superpotential

Provides a geometric interpretation of extended supersymmetry

Abstract

We show that $N=2$ and $N=4$ extended supersymmetric Yang-Mills theories in four space-time dimensions could be derived as action functionals for non-commutative spaces. The coupling of $N=1$ and $N=2$ super Yang-Mills to $N=1$ and $N=2$ matter could be derived as action functionals of non-commutative spaces only for a restricted class of models where a general superpotential is not allowed.