Affine Toda Systems Coupled to Matter Fields

TL;DR

This paper explores integrable affine Toda models coupled with matter fields, revealing soliton solutions that exhibit confinement and potential applications to QCD and electron localization.

Contribution

It introduces higher grading affine Toda systems with matter fields obeying Dirac-like equations, and uncovers a special subclass with a topologically linked Noether current.

Findings

Existence of soliton solutions with confined matter fields.

Identification of a subclass with a topological current proportional to a U(1) charge.

Relevance to one-dimensional bag models for QCD and electron-phonon systems.

Abstract

We investigate higher grading integrable generalizations of the affine Toda systems. The extra fields, associated to non zero grade generators, obey field equations of the Dirac type and are regarded as matter fields. The models possess soliton configurations, which can be interpreted as particles of the theory, on the same footing as those associated to fundamental fields. A special subclass of these models is remarkable. They possess a $U(1)$ Noether current which, after a special gauge fixing of the conformal symmetry, is proportional to a topological current. This leads to the confinement of the matter field inside the solitons, which can be regarded as a one dimensional bag model for QCD. These models are also relevent to the study of electron self--localization in (quasi)-one-dimensional electron--phonon systems.