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

We present solutions of the Yang-Mills equation on cylinders $\mathbb R\times G/H$overcosetspaceswithSasakianstructureandodddimension$2m+1$. 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 $S^1\times G\mathrm{/}H$ and dyon solutions on $i\mathbb{R}\times G\mathrm{/}H$.