Generalized Two-Dimensional QCD

TL;DR

This paper extends the analysis of two-dimensional gauge theories with fermions, generalizing bosonization and large N solutions, and explores their relevance to string theory and higher-dimensional QCD.

Contribution

It introduces a generalized framework for two-dimensional QCD with various gauge groups and potentials, extending known solutions and methods.

Findings

Bosonization of the Schwinger model is generalized for a broader class of potentials.

A natural generalization of 't Hooft's large N solution for SU(N) theories is proposed.

Potential connections to string theory and higher-dimensional QCD are discussed.

Abstract

We study two-dimensional gauge theories with fundamental fermions and a general first order gauge-field Lagrangian. For the case of U(1) we show how standard bosonization of the Schwinger model generalizes to give mesons interacting through a general Landau-Ginzburg potential. We then show how for a subclass of SU(N) theories, 't Hooft's solution of large N two-dimensional QCD can be generalized in a consistent and natural manner. We finally point out the possible relevance of studying these theories to the string formulation of two-dimensional QCD as well as to understanding QCD in higher dimensions.