Jacobi Elliptic Monopole-Antimonopole Pair Solutions

TL;DR

This paper introduces new classical monopole-antimonopole pair solutions in SU(2) Yang-Mills-Higgs theory, characterized by Jacobi elliptic functions, with energies comparable to single monopole solutions and confirmed as regular finite energy non-BPS solutions.

Contribution

The paper presents novel generalized Jacobi elliptic monopole-antimonopole pair solutions with varying winding numbers, extending previous solutions and solving the equations numerically for different Higgs potential parameters.

Findings

Solutions are regular, finite energy, non-BPS configurations.

Total energies are comparable to single monopole solutions, lower than double monopole energies.

Solutions are obtained numerically for both vanishing and non-vanishing Higgs potential.

Abstract

We present new classical generalized Jacobi elliptic one monopole - antimonopole pair (MAP) solutions of the SU(2) Yang-Mills-Higgs theory with the Higgs field in the adjoint representation. These generalized 1-MAP solutions are solved with $\theta$-winding number $m$=1 and $\phi$-winding number $n$=1, 2, 3, ... 6. Similar to the generalized Jacobi elliptic one monopole solutions, these generalized 1-MAP solutions are solved by generalizing the large distance behaviour of the solutions to the Jacobi elliptic functions and solving the second order equations of motion numerically when the Higgs potential is vanishing ($\lambda$=0) and non vanishing ($\lambda$=1). These generalized 1-MAP solutions possess total energies that are comparable to the total energy of the standard 1-MAP solution with winding number $m$=1. However these total energies are significantly lower than the total energy of the standard 1-MAP solution with winding number $m$=2. All these new generalized solutions are regular numerical finite energy non-BPS solutions of the Yang-Mills-Higgs field theory.