Integrability and duality in two-dimensional QCD

TL;DR

This paper demonstrates that bosonized two-dimensional QCD exhibits integrability in both weak and strong coupling regimes, and explores the duality transformation and constraints ensuring a positive metric Hilbert space.

Contribution

It proves integrability conditions for bosonized QCD2 and introduces a duality transformation to describe the strong coupling limit while maintaining integrability.

Findings

Existence of an integrability condition in quantum bosonized QCD2.

A duality transformation leading to an integrable description of the strong coupling regime.

Constraints ensuring a positive metric Hilbert space in the model.

Abstract

We consider bosonized $QCD_2$, and prove that after rewritting the theory in terms of gauge invariant fields, there exists an integrability condition valid for the quantum theory as well. Furthermore, performing a duality type transformation we obtain an appropriate action for the description of the strong coupling limit, which is still integrable. We also prove that the model displays a complicated set of constraints, restricting the dynamics of part of the theory, but which are necessary to maintain the positive metric Hilbert space.