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

Maike Tormählen

doi:10.1016/j.nuclphysb.2015.11.013

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arXiv · 1412.7069

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

Maike Tormählen

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

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Maike Tormählen. 2015-12-11. Yang-Mills Solutions and Dyons on Cylinders over Coset Spaces with Sasakian Structure. https://doi.org/10.1016/j.nuclphysb.2015.11.013

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