Attractive and repulsive Yang-Mills--Higgs magnetic monopoles on $\mathbb{R}^3$

TL;DR

This paper introduces an $SO(3)$-gauged Higgs model on $ olinebreak \\mathbb{R}^3$ that exhibits both attractive and repulsive phases, stabilized by a novel Higgs Chern-Pontryagin charge, differing from traditional models.

Contribution

The model uniquely stabilizes energy using a Higgs analogue of the Chern-Pontryagin charge, unlike previous models relying on the Higgs--Chern-Pontryagin charge.

Findings

Features both attractive and repulsive phases.

Solutions do not saturate the topological lower bound.

Energy stabilization via a new Higgs Chern-Pontryagin charge.

Abstract

An $SO(3)$-gauged Higgs model on $\mathbb{R}^3$ is proposed that, like the Abelian Higgs model on $\mathbb{R}^2$, features both attractive and repulsive phases, though unlike the latter its solutions do not saturate the topological lower bound. What distinguishes this model is that its energy is stabilised by the "Higgs analogue of the Chern-Pontryagin" charge, rather than the usual "Higgs--Chern-Pontryagin" charge which is a dimensional descendant of the Chern-Pontryagin charge.