Tunneling in two dimensional QCD

TL;DR

This paper investigates the critical behavior in two-dimensional continuum QCD, revealing that winding Wilson loops encode a tunneling process between different regimes, which may also be relevant for four-dimensional QCD.

Contribution

It demonstrates how the critical area in 2D QCD is reflected in winding Wilson loops through a tunneling interpretation, connecting non-analytic spectral density to loop dynamics.

Findings

Critical area affects winding Wilson loops without non-analyticity.

Existence of a tunneling process between ordered and disordered states.

Potential relevance of tunneling in 4D QCD as suggested by recent studies.

Abstract

The spectral density for two dimensional continuum QCD has a non-analytic behavior for a critical area. Apparently this is not reflected in the Wilson loops. However, we show that the existence of a critical area is encoded in the winding Wilson loops: Although there is no non-analyticity or phase transition in these Wilson loops, the dynamics of these loops consists of two smoothly connected domains separated by the critical area, one domain with a confining behavior for large winding Wilson loops, and one (below the critical size) where the string tension disappears. We show that this can be interpreted in terms of a simple tunneling process between an ordered and a disordered state. In view of recent results by Narayanan and Neuberger this tunneling may also be relevant for four dimensional QCD.