Monopoles, instantons and the Helmholtz equation
arXiv:1603.09575 · doi:10.1063/1.4955418
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.
18 pages, 3 figures