Towards a solution of two dimensional QCD

TL;DR

This paper bosonizes two-dimensional QCD, demonstrating its integrability, analyzing vacuum structure, and proposing an exact S-matrix for physical excitations, thus advancing understanding of non-perturbative aspects of 2D gauge theories.

Contribution

It provides a bosonized formulation of QCD$_2$, proves its integrability, and constructs an exact S-matrix, offering new insights into the theory's non-perturbative structure.

Findings

QCD$_2$ can be expressed as a product of WZW models and perturbations.

The model is proven to be integrable with higher conservation laws.

A finite number of vacua exist in the theory.

Abstract

Using the well-known result for the fermionic determinant in terms of a WZW theory, we write QCD$_2$ in bosonized form. After some manipulations we give two versions of the theory, where it is factorized as a product of the conformally invariant WZW models, ghost terms, and a WZW action perturbed off criticality. We first prove that the latter is an integrable model. Furthermore, as a consequence of the BRST analysis, there are several constraints. Second-class constraints also show up. Using the integrability condition we find higher conservation laws, their action on the asymptotic states, and we propose an exact $S$-matrix for the physical excitations. The vacuum structure is analysed, and we prove that a finite number of different vacua exist. An outline of possible generalizations of the procedure is given.