Construction of multi-instantons in eight dimensions

TL;DR

This paper develops a framework for constructing multi-instanton solutions in eight-dimensional space using octonionic gauge theory, extending the ADHM method to higher dimensions and revealing new classes of solutions.

Contribution

It introduces a novel 8D instanton construction based on octonions, generalizing the ADHM method for multi-instantons in higher dimensions.

Findings

Found explicit multi-instanton solutions depending on 16k-7 parameters.

Established duality relations between two- and four-forms in 8D.

Extended the ADHM construction to eight dimensions.

Abstract

We consider an eight-dimensional local octonionic theory with the seven-sphere playing the role of the gauge group. Duality conditions for two- and four-forms in eight dimensions are related. Dual fields--octonionic instantons--solve an 8D generalization of the Yang-Mills equation. Modifying the ADHM construction of 4D instantons, we find general $k$-instanton 8D solutions which depends on $16k-7$ effective parameters.