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arXiv · 1603.09575

Monopoles, instantons and the Helmholtz equation

Guido Franchetti·Rafael Maldonado
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Abstract

In this work we study the dimensional reduction of smooth circle invariant Yang-Mills instantons defined on 4-manifolds which are non-trivial circle fibrations over hyperbolic 3-space. A suitable choice of the 4-manifold metric within a specific conformal class gives rise to singular and smooth hyperbolic monopoles. A large class of monopoles is obtained if the conformal factor satisfies the Helmholtz equation on hyperbolic 3-space. We describe simple configurations and relate our results to the JNR construction, for which we provide a geometric interpretation.

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Guido Franchetti, Rafael Maldonado. 2016-03-31. Monopoles, instantons and the Helmholtz equation. https://doi.org/10.1063/1.4955418

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