Solitons as baryons and qualitons as constituent quarks in two-dimensional QCD

TL;DR

This paper explores soliton solutions in two-dimensional QCD, demonstrating their role as baryons and quarks, and analyzing how quark confinement and constituent quarks emerge in this simplified model.

Contribution

It classifies soliton solutions in the generalized sine-Gordon model and links them to quark confinement and constituent quarks in 2D QCD.

Findings

Solitons represent baryons and exotic states in 2D QCD.

Quark soliton solutions exist for sufficiently large quark mass.

Confinement of spinors inside solitons models quark confinement.

Abstract

We study the soliton type solutions arising in two-dimensional quantum chromodynamics (QCD$_{2}$). The so-called generalized sine-Gordon model (GSG) arises as the low-energy effective action of bosonized QCD$_{2}$ for unequal quark mass parameters, and it has been shown that the relevant solitons describe the normal and exotic baryonic spectrum of QCD$_{2}$ [JHEP(03)(2007)(055)]. In the first part of this chapter we classify the soliton and kink type solutions of the sl(3) GSG model. Related to the GSG model we consider the sl(3) affine Toda model coupled to matter fields (Dirac spinors) (ATM). It has been shown the confinement of the spinors inside the solitons and kinks of the GSG model providing an extended hadron model for "quark" confinement [JHEP(01)(2007)(027)]. In the second part of this chapter we discuss the appearance of the constituent quarks in the context of bosonized QCD$_{2}$ and the relevance of the $sl(2)$ ATM model in order to describe the confinement of the color degrees of freedom. We have shown that QCD$_{2}$ has quark soliton solutions if the quark mass is sufficiently large.