On a class of gauge theories

TL;DR

This paper introduces a novel gauge theory framework replacing the traditional structure group with a nonassociative Moufang loop, extending gauge invariance and constructing an on-shell N=1 supersymmetric version.

Contribution

It presents a new formalism for gauge theories using Moufang loops, expanding the mathematical foundation and including supersymmetric extensions.

Findings

Framework for gauge theories with Moufang loops

Extension of gauge invariance to nonassociative structures

Construction of on-shell N=1 supersymmetric gauge theory

Abstract

We give a framework to describe gauge theory in which a nonassociative Moufang loop takes the place of the structure group. The structure of such gauge theory has many formal similarities with that of Yang-Mills theory. We extend the gauge invariance to this theory and construct an on-shell version of N=1 supersymmetric gauge theory.