Bosonization and QCD in Two Dimensions

TL;DR

This paper reviews bosonization techniques applied to two-dimensional QCD, detailing abelian and non-abelian methods, and explores the low-energy baryonic spectrum through classical solutions and quantization.

Contribution

It provides a comprehensive application of bosonization to 2D QCD, including the derivation of baryonic spectra and multibaryonic solutions, extending previous methods with new insights.

Findings

Derived classical soliton solutions for baryons

Quantized flavor space to obtain baryon masses

Presented multibaryonic solutions and wave functions

Abstract

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 QCD$_2$. 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 details 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 QCD is written down. The strong coupling limit is taken in the ``product scheme" and then in the $U(N_F\times N_C)$ scheme. Once the multiflavor $QCD_2$ action in the interesting region of the low energies is written down, we extract the semiclassical low lying baryonic spectrum. First classical soliton solutions of 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 $q\bar q$ content.