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

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.