Singular Monopoles from Cheshire Bows

TL;DR

This paper introduces a new method using Cheshire bows to construct singular monopoles, overcoming limitations of Nahm's construction, and provides explicit solutions for U(2) monopoles with multiple singularities.

Contribution

The paper presents an alternative bow-based construction for singular monopoles, enabling explicit solutions for complex configurations beyond previous methods.

Findings

Explicit expression for U(2) monopoles with multiple singularities

Demonstration of advantages over Nahm's construction

Extension of monopole solutions to arbitrary singularity counts

Abstract

Singular monopoles are nonabelian monopoles with prescribed Dirac-type singularities. All of them are delivered by the Nahm's construction. In practice, however, the effectiveness of the latter is limited to the cases of one or two singularities. We present an alternative construction of singular monopoles formulated in terms of Cheshire bows. To illustrate the advantages of our bow construction we obtain an explicit expression for one U(2) gauge group monopole with any given number of singularities of Dirac type.