Monopole-Antimonopole and Vortex Rings

TL;DR

This paper presents new exact static solutions in SU(2) Yang-Mills-Higgs theory featuring monopole-antimonopole configurations with vortex rings, revealing complex structures and singularities that expand understanding of topological solitons.

Contribution

It introduces novel exact static A-M-A configurations with vortex rings and analyzes their properties, including monopole structures and singularities, within the Yang-Mills-Higgs framework.

Findings

Net magnetic charge is always negative one.

Vortex rings appear with increasing parameter m.

Solutions satisfy Bogomol'nyi equations but have infinite energy.

Abstract

The SU(2) Yang-Mills-Higgs theory supports the existence of monopoles, antimonopoles, and vortex rings. In this paper, we would like to present new exact static antimonopole-monopole-antimonopole (A-M-A) configurations. The net magnetic charge of these configurations is always negative one, whilst the net magnetic charge at the origin is always positive one for all positive integer values of the solution's parameter $m$. However, when $m$ increases beyond one, vortex rings appear coexisting with these A-M-A configurations. The number of vortex rings increases proportionally with the value of $m$. They are located in space where the Higgs field vanishes along rings. We also show that a single point singularity in the Higgs field does not necessarily corresponds to a structureless 1-monopole at the origin but to a zero size monopole-antimonopole-monopole (\textcolor{blue}{MAM}) structure when the solution's parameter $m$ is odd. This monopole is the Wu-Yang type monopole and it possesses the Dirac string potential in the Abelian gauge. These exact solutions are a different kind of BPS solutions as they satisfy the first order Bogomol'nyi equation but possess infinite energy due to a point singularity at the origin of the coordinate axes. They are all axially symmetrical about the z-axis.