Some exact Bradlow vortex solutions

Abstract

We consider the Bradlow equation for vortices which was recently found by Manton and find a two-parameter class of analytic solutions in closed form on nontrivial geometries with non-constant curvature. The general solution to our class of metrics is given by a hypergeometric function and the area of the vortex domain by the Gaussian hypergeometric function.

LaTeX: 16 pages, no figures; V2: references added, minor additions; V3 (published version): toy model added as section 3 and conjecture 1 added in section 4.1

References in corpus (1)

• Synthetic magnetic fields for ultracold neutral atoms

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