All finite-mass Dirac monopoles

TL;DR

This paper introduces a simple method to realize finite-mass Dirac monopoles in $U(1)$ gauge theories with a scalar field, showing their energy distribution and connecting to various classical monopole models.

Contribution

It presents a novel construction of finite-mass Dirac monopoles using a non-minimally interacting scalar, unifying classical monopoles within a broader gauge model landscape.

Findings

Monopole energy density forms a spherical shell in the BPS limit.

Construction interprets as a limit of infinitely massive W bosons with a dipole moment.

All classical monopoles are special cases within the proposed model landscape.

Abstract

We present a "primitive" way of realizing finite-mass Dirac monopoles in $U(1)$ gauge theories involving a single non-minimally interacting scalar field. Typically, the energy density of this type of monopole is not concentrated at its core, but it is distributed in a spherical shell, as we illustrate on several exact solutions in the Bogomol'nyi-Prasad-Sommerfield (BPS) limit. We show that our construction can be interpreted as a limit of infinitely massive $W$ bosons coupled to electromagnetic field-strength via a dipole moment. Combining our approach with ideas of Weinberg and Lee, we present a general landscape of $U(1)$ gauge models that support a finite-mass Dirac monopole. In fact, all classical monopoles, i.e., Wu-Yang, 't Hooft-Polyakov, Cho-Maison, etc., are special points on this landscape.