Non-associative Gauge Theory

TL;DR

This paper constructs a gauge theory based on non-associative Moufang loops, specifically using octonions, leading to a novel octonionic gauge theory that generalizes classical gauge theories like Maxwell and Yang-Mills.

Contribution

It introduces a gauge theory framework with a non-associative structure group, expanding the scope of gauge theories beyond Lie groups.

Findings

Developed an octonionic gauge theory using Moufang loops.

Provided a BPST-like instanton solution in 8 dimensions.

Generalized classical gauge theories to non-associative algebraic structures.

Abstract

We present a construction of gauge theory which its structure group is not a Lie group, but a Moufang loop which is essentially non-associative. As an example of non-associative algebra, we take octonions with norm one as a Moufang loop, with which we can produce an octonionic gauge theory. Our octonionic gauge theory is a natural generalization of Maxwell U(1)= S^1 gauge theory and Yang-Mills SU(2)= S^3 gauge theory. We also give the BPST like instanton solution of our octonionic gauge theory in 8 dimension.