Solitons, kinks and extended hadron model based on the generalized sine-Gordon theory

TL;DR

This paper explores the generalized sine-Gordon model based on sl(3,C), deriving soliton solutions, analyzing properties, and proposing an extended hadron model illustrating quark confinement through solitons and kinks.

Contribution

It provides explicit soliton solutions for the generalized sl(3,C) sine-Gordon model and constructs an extended hadron model demonstrating quark confinement.

Findings

Explicit soliton and kink solutions derived.

The model exhibits quark confinement within solitons.

Reduced double sine-Gordon submodel identified.

Abstract

The solitons and kinks of the generalized $sl(3, \IC)$ sine-Gordon (GSG) model are explicitly obtained through the hybrid of the Hirota and dressing methods in which the {\sl tau} functions play an important role. The various properties are investigated, such as the potential vacuum structure, the soliton and kink solutions, and the soliton masses formulae. As a reduced submodel we obtain the double sine-Gordon model. Moreover, we provide the algebraic construction of the $sl(3, \IC)$ affine Toda model coupled to matter (Dirac spinor) (ATM) and through a gauge fixing procedure we obtain the classical version of the generalized $sl(3, \IC)$ sine-Gordon model (cGSG) which completely decouples from the Dirac spinors. In the spinor sector we are left with Dirac fields coupled to cGSG fields. Based on the equivalence between the U(1) vector and topological currents it is shown the confinement of the spinors inside the solitons and kinks of the cGSG model providing an extended hadron model for "quark" confinement.