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

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 $i\mathbb{R}\times G/H$.

30 pages, 4 figures

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• Four-dimensional String Compactifications with D-Branes, Orientifolds and Fluxes
• Flux Compactification
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Cited by in corpus (1)

• Yang-Mills solutions and Spin(7)-instantons on cylinders over coset spaces with $G_2$-structure