Noncommutative Instantons in 4k Dimensions

TL;DR

This paper extends classical instanton solutions to higher-dimensional noncommutative spaces using an extended ADHM construction, revealing new configurations that generalize known instantons and include novel solutions even in the commutative case.

Contribution

It introduces explicit solutions for higher-dimensional noncommutative instantons using an extended ADHM method, generalizing known four-dimensional instantons.

Findings

Explicit solutions for noncommutative instantons in 4k dimensions

Generalization of 't Hooft and BPST instantons to higher dimensions

Discovery of new BPST-type configurations in the commutative limit

Abstract

We consider Ward's generalized self-duality equations for U(2r) Yang-Mills theory on R^{4k} and their Moyal deformation under self-dual noncommutativity. Employing an extended ADHM construction we find two kinds of explicit solutions, which generalize the 't Hooft and BPST instantons from R^4 to noncommutative R^{4k}. The BPST-type configurations appear to be new even in the commutative case.