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

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.