Singular Monopoles via the Nahm Transform

TL;DR

This paper derives explicit solutions for charge one BPS monopoles with two Dirac singularities using the Nahm transform, expanding the known solution space and exploring various limits.

Contribution

It provides the first explicit expressions for these monopoles with singularities via the Nahm transform, enhancing understanding of their structure.

Findings

Explicit monopole solutions with two Dirac singularities

New solutions obtained through various limits

Application of Nahm transform to singular monopoles

Abstract

We present explicit expressions for the fields of a charge one BPS monopole with two Dirac singularities. These are solutions of the nonlinear Bogomolny equations with the gauge group U(2) or SO(3). We derive these expressions by applying the technique of the Nahm transform. By exploring various limits we find a number of other solutions.