Dynamics of slender monopoles and anti-monopoles in non-Abelian superconductor

TL;DR

This paper explores the low-energy behavior of monopoles and anti-monopoles in a non-Abelian superconductor, revealing their scattering dynamics, bound states, and a mapping to the sine-Gordon system for simplified visualization.

Contribution

It provides analytical solutions for monopole-anti-monopole interactions and demonstrates their complex scattering behaviors in a non-Abelian superconductor.

Findings

Monopoles are slender ellipsoids pierced by vortex strings.

Monopoles and anti-monopoles can repel, form bound states, or resonances.

Solutions can be mapped onto the sine-Gordon system for easier analysis.

Abstract

Low energy dynamics of magnetic monopoles and anti-monopoles in the U(2) gauge theory is studied in the Higgs (non-Abelian superconducting) phase. The monopoles in this superconducting phase are not spherical but are of slender ellipsoid which are pierced by a vortex string. We investigate scattering of the slender monopole and anti-monopole, and find that they do not always decay into radiation, contrary to our naive intuition. They can repel, make bound states (magnetic mesons) or resonances. Analytical solutions including any number of monopoles and anti-monopoles are obtained in the first non-trivial order of rigid-body approximation. We point out that some part of solutions of slender monopole system in 1+3 dimensions can be mapped exactly onto the sine-Gordon system in 1+1 dimensions. This observation allows us to visualize dynamics of monopole and anti-monopole scattering easily.