Existence and uniqueness of generalized monopoles in six-dimensional non-Abelian gauge theory

TL;DR

This paper proves the existence and uniqueness of spherically symmetric monopole solutions in six-dimensional SO(5) gauge theory, providing sharp asymptotic estimates using a dynamical shooting method.

Contribution

It introduces a novel dynamical shooting approach to establish monopole existence and uniqueness in six-dimensional non-Abelian gauge theory.

Findings

Proved existence and uniqueness of monopoles in 6D SO(5) gauge theory.

Derived sharp asymptotic estimates for solutions.

Developed an effective shooting method for constructing monopoles.

Abstract

In this paper, we established the existence and uniqueness of the spherically symmetric monopole solutions in SO(5) gauge theory with Higgs scalar fields in the vector representation in six-dimensional Minkowski space-time and obtain sharp asymptotic estimates for the solutions. Our method is based on a dynamical shooting approach that depends on two shooting parameters which provides an effective framework for constructing the generalized monopoles in six-dimensional Minkowski space-time.