Connection between Space-Time Supersymmetry and Non-Commutative Geometry

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.