One-dimensional dynamics of QCD2 string

TL;DR

This paper introduces a one-dimensional model of QCD$_2$ string dynamics that exhibits a third-order phase transition and could serve as a simplified model for understanding glueball thresholds in multicolor QCD.

Contribution

It presents a novel one-dimensional evolution model of the QCD$_2$ string consistent with the Gross-Taylor string picture, revealing a third-order phase transition and connections to matrix models.

Findings

Identifies a third-order phase transition in the model.

Shows equivalence to the vortex-free sector of a 1D matrix model.

Proposes the model as a toy for glueball threshold behavior.

Abstract

We show that QCD$_2$ on 2D pseudo-manifolds is consistent with the Gross-Taylor string picture. It allows us to introduce a model describing the one-dimensional evolution of the QCD$_2$ string (in the sense that QCD$_2$ itself is regarded as a zero-dimensional system). The model is shown to possess the third order phase transition associated with the $c=1$ Bose string below which it becomes equivalent to the vortex-free sector of the 1-dimensional matrix model. We argue that it could serve as a toy model for the glueball-threshold behavior of multicolor QCD.