Monopole-Antimonopole Pair Dyons with Critical Electric Charges

TL;DR

This paper numerically investigates axially symmetric, non-BPS monopole-antimonopole pair dyons in SU(2) Yang-Mills-Higgs theory, analyzing their electric charges, energies, and dipole moments near critical charge values.

Contribution

It introduces a new class of stationary, non-BPS dyon solutions with finite energy and critical electric charges, characterized by axial symmetry and specific Higgs field configurations.

Findings

Electric charge approaches a finite critical value as parameter approaches ±1.

Total energy and magnetic dipole moment also reach finite critical values.

Solutions are numerically obtained for magnetic charges n=1 to 5 with non-zero Higgs potential.

Abstract

In this paper, we investigate some electrically charged magnetic solutions of the SU(2) Yang-Mills-Higgs field theory in the net zero topological charge sector. We only examine the case when the Higgs field vanishes at two points along the z-axis and when the Higgs field vanishes along a ring with the z-axis as its symmetry axis. We study the possible electric charges the dyons can carry in relation to the electric-magnetic charge separations and calculate for the finite total energy and magnet dipole moment of these dyons. These stationary dyon solutions do not satisfy the first order Bogomol'nyi equations and are non BPS solutions. They are axially symmetric saddle point solutions and are characterized by the electric charge parameter, $-1<\eta< 1$, which determines the net electric charges of these dyons. These dyon solutions are solved numerically when the magnetic charges are $n$ = 1, 2, 3, 4, and 5; and when the strength of the Higgs field potential is non vanishing with $\lambda=1$. When $\lambda=1$, we found that the net electric charge approaches a finite critical value as $\eta$ approaches $\pm 1$. Hence the electromagnetic charge separation, total energy, and magnet dipole moment of the dyon also approach finite critical value.