Instantons and Yang-Mills Flows on Coset Spaces

TL;DR

This paper studies Yang-Mills equations and flows on coset spaces G/H, deriving explicit solutions including instantons, dyons, and kink solutions, with a focus on geometric fluxes and torsion effects.

Contribution

It introduces explicit solutions to Yang-Mills and flow equations on coset spaces, incorporating torsion and geometric fluxes, and explores their physical interpretations.

Findings

Explicit instanton and dyon solutions on G/H

Reduction of Yang-Mills equations to phi^4-kink equations

Comparison of Yang-Mills flow solutions with static solutions

Abstract

We consider the Yang-Mills flow equations on a reductive coset space G/H and the Yang-Mills equations on the manifold R x G/H. On nonsymmetric 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 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 R x 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 R x G/H.