Instantons and Yang–Mills Flows on Coset Spaces

Abstract

We consider the Yang–Mills flow equations on a reductive coset space G/H and the Yang–Mills equations on the manifold \({\mathbb{R}\times G/H}\). On non-symmetric coset spaces G/H one can introduce geometric fluxes identified with the torsion of the spin connection. The condition of G-equivariance imposed on the gauge fields reduces the Yang–Mills equations to \({\phi^4}\)-kink equations on \({\mathbb{R}}\). Depending on the boundary conditions and torsion, we obtain solutions to the Yang–Mills equations describing instantons, chains of instanton–anti-instanton pairs or modifications of gauge bundles. For Lorentzian signature on \({\mathbb{R}\times G/H}\), dyon-type configurations are constructed as well. We also present explicit solutions to the Yang–Mills flow equations and compare them with the Yang–Mills solutions on \({\mathbb{R}\times G/H}\).