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

TL;DR

This paper derives N=2 and N=4 super Yang-Mills theories from a gauge theory perspective on a discrete space, interpreting scalars as gauge fields along extra discrete dimensions.

Contribution

It introduces a novel geometric framework for super Yang-Mills theories using a discrete extra-dimensional space, providing new insights into their structure.

Findings

Super Yang-Mills theories are derived from a gauge theory on a discrete space.

Scalars and pseudoscalars are interpreted as gauge fields along discrete directions.

The approach offers a geometric understanding of supersymmetric gauge theories.

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.