Monopole-Antimonopole Chains and Vortex Rings

TL;DR

This paper explores static axially symmetric solutions in SU(2) Yang-Mills-Higgs theory, revealing monopole-antimonopole chains and vortex rings, analyzing their properties, energies, and effects of Higgs self-coupling.

Contribution

It introduces and characterizes new monopole-antimonopole chain and vortex ring solutions, detailing their properties and the influence of Higgs self-coupling.

Findings

Monopole-antimonopole chains exist with Higgs field vanishing at points.

Vortex rings form with Higgs field vanishing on rings.

Finite Higgs self-coupling affects solution properties.

Abstract

We consider static axially symmetric solutions of SU(2) Yang-Mills-Higgs theory. The simplest such solutions represent monopoles, multimonopoles and monopole-antimonopole pairs. In general such solutions are characterized by two integers, the winding number m of their polar angle, and the winding number n of their azimuthal angle. For solutions with n=1 and n=2, the Higgs field vanishes at m isolated points along the symmetry axis, which are associated with the locations of m monopoles and antimonopoles of charge n. These solutions represent chains of m monopoles and antimonopoles in static equilibrium. For larger values of n, totally different configurations arise, where the Higgs field vanishes on one or more rings, centered around the symmetry axis. We discuss the properties of such monopole-antimonopole chains and vortex rings, in particular their energies and magnetic dipole moments, and we study the influence of a finite Higgs self-coupling constant on these solutions.