Yang-Mills like instantons in eight and seven dimensions

TL;DR

This paper explores gauge theories with nonassociative structures in seven and eight dimensions, constructing instanton solutions analogous to classic BPST and t'Hooft instantons.

Contribution

It introduces instanton solutions in higher dimensions using nonassociative Moufang loops, extending the scope of gauge theory solutions beyond traditional groups.

Findings

Constructed BPST-like instantons in seven and eight dimensions.

Developed t'Hooft-like instanton solutions in higher dimensions.

Extended gauge theory frameworks to include nonassociative algebraic structures.

Abstract

We consider a gauge theory in which a nonassociative Moufang loop takes the place of a structure group. We construct Belavin-Polyakov-Schwartz-Tyupkin (BPST) and t'Hooft like instanton solutions of the gauge theory in seven and eight dimensions.