Constraining Monopoles by Topology: an Autonomous System

TL;DR

This paper presents analytical and numerical solutions for SU(2) Yang-Mills theories with an adjoint Higgs field in tube-shaped geometries, revealing new monopole and dyon configurations and long-lived breather states.

Contribution

It introduces novel analytical solutions for monopoles and dyons in curved tube geometries with non-zero Higgs coupling, expanding understanding of topological constraints.

Findings

Analytical solutions for monopoles and dyons in tube geometries.

Existence of long-lived breather states in the system.

Smooth limit to flat space enabling analytical tools.

Abstract

We find both analytical and numerical solutions of SU(2) Yang-Mills with an adjoint Higgs field within both closed and open tubes whose sections are spherical caps. This geometry admits a smooth limit in which the space-like metric is flat and, moreover, allows one to use analytical tools which in the flat case are not available. Some of the analytic configurations, in the limit of vanishing Higgs coupling, correspond to magnetic monopoles and dyons living within this tube-shaped domain. However, unlike what happens in the standard case, analytical solutions can also be found in the case in which the Higgs coupling is non-vanishing. We further show that the system admits long-lived breathers.