Yang-Mills Solutions and Dyons on Cylinders over Coset Spaces with Sasakian Structure

TL;DR

This paper constructs and analyzes explicit Yang-Mills solutions, including instantons, sphalerons, and dyons, on cylinders over Sasakian coset spaces, revealing their structure through reduced Newtonian mechanics.

Contribution

It introduces a novel approach to solving Yang-Mills equations on Sasakian coset spaces by reducing them to Newtonian mechanics and constructs various explicit solutions.

Findings

Analytic and numerical finite-action solutions found.

Construction of periodic sphaleron solutions.

Construction of dyon solutions on cylinders over coset spaces.

Abstract

We present solutions of the Yang-Mills equation on cylinders $\mathbb R\times G/H$ over coset spaces with Sasakian structure and odd dimension $2m+1$. The gauge potential is assumed to be $SU(m)$-equivariant, parametrized by two real, scalar-valued functions. Yang-Mills theory with torsion in this setup reduces to the Newtonian mechanics of a point particle moving in $\mathbb R^2$ under the influence of an inverted potential. We analyze the critical points of this potential and present an analytic as well as several numerical finite-action solutions. Apart from the Yang-Mills solutions that constitute $SU(m)$-equivariant instanton configurations, we construct periodic sphaleron solutions on $S^1\times G/H$ and dyon solutions on $i\mathbb R\times G/H$.