Bifurcating Branches of Multiple Charged One-Plus-Half Monopole In SU(2) Yang-Mills-Higgs Theory

TL;DR

This study explores complex monopole configurations in SU(2) Yang-Mills-Higgs theory, revealing bifurcations, transitions, and new vortex-ring solutions as the Higgs coupling varies for monopoles with different winding numbers.

Contribution

It uncovers bifurcation phenomena and the existence of new vortex-ring branches in monopole solutions for higher winding numbers in SU(2) Yang-Mills-Higgs theory.

Findings

Bifurcation and transition occur for n > 2 at critical Higgs coupling values.

Multiple energy branches, including a new vortex-ring branch, are identified.

Finite energy solutions with detailed density plots are presented.

Abstract

In this paper, we study on the one-plus-half monopole configuration in SU(2) Yang-Mills-Higgs theory when the $\phi$-winding number, $n$, runs from 2 to 4 and for a range of Higgs coupling constant, $\lambda_b \leq \lambda \leq 40$, where $\lambda_b$ is the lower bound, below which no solution can be found. Bifurcation and transition are observed for $n > 2$ when the Higgs coupling constant is larger than some critical value $\lambda_c$ and transitional value $\lambda_t$, respectively. Two different branches with energy higher than the fundamental solution are observed for both $n = 3$ and $4$. We also observed a new branch with even higher energy for $n = 4$. Unlike other branches which display transition behavior, the new branch corresponds to a full vortex-ring configuration. All the solutions possess finite energy. Plots of magnetic charge density, Higgs modulus and energy density are presented and analyzed.