Self-Duality Equations on S^6 from R^7 monopole

TL;DR

This paper establishes a connection between monopole solutions in seven dimensions and self-dual Yang-Mills configurations on a six-dimensional sphere, linking topological charges to homotopy groups.

Contribution

It identifies a novel correspondence between 7D monopoles and 6D self-dual configurations, enriching the understanding of gauge theories in higher dimensions.

Findings

Topological charge relates to the sixth homotopy group of G/H.

A correspondence between 7D monopoles and 6D self-duality is established.

The work extends the understanding of gauge configurations in higher dimensions.

Abstract

In this note we identify a correspondence between a seven-dimensional monopole configuration of the Yang-Mills-Higgs system and the generalized self-dual configuration of the Yang-Mills system on a six-dimensional sphere. In particular, the topological charge of the self-duality configurations belongs to the sixth homotopy group of the coset G/H associated with the symmetry breaking G -> H induced by a non-trivial Higgs configuration in seven-dimensions.