Construction of multi-instantons in eight dimensions

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.