Generalized Jacobi Elliptic One-Monopole - Type A

TL;DR

This paper introduces a new class of axially symmetric, finite-energy monopole solutions in SU(2) Yang-Mills-Higgs theory, generalizing the 't Hooft-Polyakov monopole using Jacobi elliptic functions, and explores their properties numerically.

Contribution

It presents the first Jacobi elliptic generalization of the 't Hooft-Polyakov monopole with detailed construction and numerical analysis.

Findings

New axially symmetric monopole solutions with Jacobi elliptic functions.

Regular non-BPS finite energy solutions.

Generalization applicable to both vanishing and non-vanishing Higgs potentials.

Abstract

We present new classical generalized one-monopole solution of the SU(2) Yang-Mills-Higgs theory with the Higgs field in the adjoint representation. We show that this generalized solution with $\theta$-winding number $m=1$ and $\phi$-winding number $n=1$ is an axially symmetric Jacobi elliptic generalization of the 't Hooft-Polyakov one-monopole. We construct this axially symmetric one-monopole solution by generalizing the large distance asymptotic solution of the 't Hooft-Polyakov one-monopole to the Jacobi elliptic functions and solving the second order equations of motion numerically when the Higgs potential is vanishing and non vanishing. These solutions are regular non-BPS finite energy solutions.