Dyon and magnetic monopole in Yang--Mills theory derived through the complementary gauge-scalar model

TL;DR

This paper demonstrates the gauge-independent construction of dyons and magnetic monopoles in pure SU(2) Yang-Mills theory, linking topological configurations to quark confinement without requiring scalar fields.

Contribution

It introduces a method to derive monopoles and dyons in Yang-Mills theory independently of scalar fields, advancing understanding of topological configurations in confinement.

Findings

Constructed monopoles and dyons without scalar fields

Linked topological configurations to quark confinement

Provided a gauge-independent framework for these solutions

Abstract

We show that dyon and magnetic monopole can be constructed in the gauge-independent way for the $SU(2)$ Yang--Mills theory even in the absence of the scalar field. This result is derived from the recent proposal for obtaining non-trivial topological configurations responsible for quark confinement in the Yang-Mills theory based on the Confinement-Higgs complementary relationship between the pure Yang-Mills theory and the gauge-scalar model with an adjoint scalar field of the fixed length. We discuss how such configurations have the implications for quark confinement.