Comments on the Monopole-Antimonopole Pair Solutions

TL;DR

This paper numerically studies monopole-antimonopole pair solutions in SU(2) Yang-Mills-Higgs theory with a focus on solutions with theta-winding number one, revealing parameterization by a single integer at different distances.

Contribution

It demonstrates the existence of monopole-antimonopole solutions with theta-winding number one and characterizes their asymptotic behavior using a single parameter.

Findings

Solutions with theta-winding number one exist in the topologically trivial sector.

Asymptotic solutions are parameterized by a single integer at small and large distances.

The solutions transition from s=0 at small r to s=1 at large r.

Abstract

Recently, the monopole-antimonopole pair and monopole-antimonopole chain solutions are solved with internal space coordinate system of $\theta$-winding number $m$ greater than one. However, we notice that it is also possible to solve these solutions numerically in terms of $\theta$-winding number $m=1$ instead. When $m=1$, the exact asymptotic solutions at small and large distances are parameterized by a single integer parameter $s$. Here we once again study the monopole-antimonopole pair solution of the SU(2) Yang-Mills-Higgs theory which belongs to the topological trivial sector numerically in its new form. This solution with $\theta$-winding and $\phi$-winding number one is parameterized by $s=0$ at small $r$ and $s=1$ at large $r$.