Monopole-Antimonopole Pair Dyons

TL;DR

This paper presents numerical solutions for monopole-antimonopole pair dyons with electric and magnetic charges, analyzing their properties and behaviors under different parameters and Higgs potential strengths.

Contribution

It introduces finite-energy MAP dyon solutions that are not BPS and explores their characteristics across various magnetic charges and Higgs potential values.

Findings

Solutions are finite energy but not BPS.

Electric charge and separation distance grow exponentially as  approaches \u00b1

For , quantities approach finite limits when  approaches 

Abstract

Monopole-antimonopole pair (MAP) with both electric and magnetic charges are presented. The MAP possess opposite magnetic charges but they carry the same electric charges. These stationary MAP dyon solutions possess finite energy but they do not satisfy the first order Bogomol'nyi equations and are not BPS solutions. They are axially symmetric solutions and are characterized by a parameter, $-1\leq\eta\leq 1$ which determines the net electric charges of these MAP dyons. These dyon solutions are solved numerically when the magnetic charges of the dipoles are $n=\pm 1, \pm 2$ and when the strength of the Higgs field potential $\lambda=0, 1$. When $\lambda=0$, the time component of the gauge field potential is parallel to the Higgs field in isospin space and the MAP separation distance, total energy and net electric charge increase exponentially fast to infinity when $\eta$ approaches $\pm 1$. However when $\lambda=1$, all these three quantities approach a finite critical value as $\eta$ approaches $\pm 1$.