In this work we study the dimensional reduction of smooth circle invariant Yang-Mills instantons defined on 4-manifolds which asymptotically become 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 Jackiw-Nohl-Rebbi construction, for which we provide a geometric interpretation.

Monopoles, instantons, and the Helmholtz equation

Franchetti G;
2016-01-01

Abstract

In this work we study the dimensional reduction of smooth circle invariant Yang-Mills instantons defined on 4-manifolds which asymptotically become 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 Jackiw-Nohl-Rebbi construction, for which we provide a geometric interpretation.
2016
Franchetti, G; Maldonado, R
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11568/1269308
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