$N=2$ and $N=4$ SUSY Yang-Mills action on $M^4\times (Z_2\oplus Z_2)$ non-commutative geometry

Abstract

We show that the $N=2$ and $N=4$ SUSY Yang-Mills action can be reformulated in the sense of non-commutative geometry on $M^4\times (Z_2\oplus Z_2)$ in a rather simple way. In this way the scalars or pseudoscalars are viewed as gauge fields along two directions in the space of one-forms on $Z_2\oplus Z_2$.