Bosonization and QCD in two dimensions

Quantum Chromodynamics (QCD) is believed to describe the strong interactions. In the asymptotic domain of large momenta, improved perturbation theory describes phenomena by use of point-like quarks and gluons. But the spectrum and wave functions are in the nonperturbative domain, for which not much can be done analytically in four dimensions. In order to develop analytical methods physicists turned to simpler models, like QCD₂, the theory in one space and one time dimensions. This review is devoted to the application of bosonization techniques to two-dimensional QCD. We start with a description of the "abelian bosonization". The methods of the abelian bosonization are applied to several examples like the Thirring model, the Schwinger model and QCD₂, The failure of this scheme to handle flavored fermions is explained. Witten's non-abelian bosonization rules are summarized including the generalization to the case of fermions with color and flavor degrees of freedom. We discuss in detail the bosonic version of the mass bilinear of colored-flavored fermions in various schemes. The color group is gauged and the full bosonized version of massive multiflavor QCD₂ is written down. The strong coupling limit is taken in the "product scheme" and then in the U(N_F × N_C) scheme. Once the multiflavor QCD₂ action in the interesting region of the low energies is written down, we extract the semiclassical low-lying baryonic spectrum. First, classical soliton solutions the bosonic action are derived. Quantizing the flavor space around those classical solutions produces the masses as well as the flavor properties of the two-dimensional baryons. In addition, low-lying multibaryonic solutions are presented, as well as wave functions and matrix elements of interest, like qq̄ content.