Integer versions of Yang-Mills theory

Abstract

In a recent paper, 't Hooft asks for an integer version of Yang-Mills theory, in the belief that this is the way the universe really is at the Planck scale. Specifically, he asks for an integer version of the gauge group of the standard model. Such groups were completely classified more than 100 years ago, and here I detail the group theory and representation theory (and some of the physics) of the specific case that I believe answers 't Hooft's question.