N=2 and N=4 SUSY Yang-Mills action on M$^{4}$ x (Z$_{2}$ + 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