Nonlinear Schrodinger solitons in massive Yang-Mills theory and partial localization of Dirac matter

TL;DR

This paper analytically demonstrates the existence of kink soliton solutions in massive SU(2) Yang-Mills theory and shows how these solutions can localize Dirac fermions, revealing a non-abelian Landau-like localization mechanism.

Contribution

It introduces a new class of soliton solutions in massive SU(2) Yang-Mills theory and explores their role in fermion localization, extending Landau localization concepts to non-abelian fields.

Findings

Existence of kink soliton solutions modulated by plane waves.

Yang-Mills configurations can trap SU(2) charged fermions.

Mechanism analogous to Landau localization in non-abelian context.

Abstract

We investigate the classical dynamics of the massive SU(2) Yang-Mills field in the framework of multiple scale perturbation theory. We show analytically that there exists a subset of solutions having the form of a kink soliton, modulated by a plane wave, in a linear subspace transverse to the direction of free propagation. Subsequently, we explore how these solutions affect the dynamics of a Dirac field possessing an SU(2) charge. We find that this class of Yang-Mills configurations, when regarded as an external field, leads to the localization of the fermion along a line in the transverse space. Our analysis reveals a mechanism for trapping SU(2) charged fermions in the presence of an external Yang-Mills field indicating the non-abelian analogue of Landau localization in electrodynamics.