Large N phase transitions under scaling and their uses

TL;DR

This paper studies large N phase transitions in Wilson loop eigenvalues across different dimensions, revealing universal properties that could connect perturbative and string theory approaches to gauge theories.

Contribution

It identifies a universal large N phase transition in Wilson loop eigenvalues and explores its potential to unify perturbative and string descriptions of gauge theories.

Findings

Eigenvalues supported on small arc for small loops

Eigenvalues cover entire circle for large loops

Universal properties of the phase transition across dimensions

Abstract

The eigenvalues of Wilson loop matrices in SU(N) gauge theories in dimensions 2,3,4 at infinite N are supported on a small arc on the unit circle centered at $z=1$ for small loops, but expand to the entire unit circle for large loops. These two regimes are separated by a large N phase transition whose universal properties are the same in d=2,3 and 4. Hopefully, this large N universality could be exploited to bridge traditional perturbation theory calculations, valid for small loops, with effective string calculations for large loops. A concrete case of such a calculation would obtain analytically an estimate of the large N string tension in terms of the perturbative scale Lambda(QCD,N).