Yang–Mills solutions and dyons on cylinders over coset spaces with Sasakian structure

Abstract

We present solutions of the Yang–Mills equation on cylinders R×G/HR×G/H over coset spaces of odd dimension 2m+12m+1 with Sasakian structure. The gauge potential is assumed to be SU(m)SU(m)-equivariant, parameterized 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 R2R2 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)SU(m)-equivariant instanton configurations, we construct periodic sphaleron solutions on S1×G/HS1×G/H and dyon solutions on iR×G/HiR×G/H.