$N=2$ and $4$ Super Yang-Mills Theories on $M_4 \times Z_2 \times Z_2$ Geometry

Abstract

We derive the $N=2$ and $4$ super Yang-Mills theories from the viewpoint of the $M_4\times Z_2\times Z_2$ gauge theory. Scalars and pseudoscalars appearing in the theories are regarded as gauge fields along the directions on $Z_2\times Z_2$ discrete space.