Confinement and soliton solutions in the SL(3) Toda model coupled to matter fields

TL;DR

This paper explores integrable SL(3) Toda models with matter fields, deriving soliton solutions, analyzing their properties, and revealing a confinement mechanism linking spinors and solitons in a conformally invariant setting.

Contribution

It introduces a new integrable SL(3) Toda model with matter fields, providing explicit soliton solutions and analyzing their interactions and confinement properties.

Findings

Explicit one- and two-soliton solutions obtained.

Soliton masses and interaction time delays calculated.

A computer program for soliton solution computation provided.

Abstract

We consider an integrable conformally invariant two dimensional model associated to the affine Kac-Moody algebra SL(3). It possesses four scalar fields and six Dirac spinors. The theory does not possesses a local Lagrangian since the spinor equations of motion present interaction terms which are bilinear in the spinors. There exists a submodel presenting an equivalence between a U(1) vector current and a topological current, which leads to a confinement of the spinors inside the solitons. We calculate the one-soliton and two-soliton solutions using a procedure which is a hybrid of the dressing and Hirota methods. The soliton masses and time delays due to the soliton interactions are also calculated. We give a computer program to calculate the soliton solutions.