Universality of large N phase transitions in Wilson loop operators in two and three dimensions

TL;DR

This paper investigates the universal behavior of large N phase transitions in Wilson loop operators across two, three, and four dimensions, deriving a scaling function in 2D and testing universality in 3D.

Contribution

It derives a large N scaling function for Wilson loops in 2D QCD and hypothesizes universality of the transition in higher dimensions, supported by numerical tests.

Findings

Derived a scaling function in 2D QCD

Hypothesized universality of phase transitions in 3D and 4D

Numerical evidence supports the universality hypothesis

Abstract

The eigenvalue distribution of a Wilson loop operator of fixed shape undergoes a transition under scaling at infinite N. We derive a large N scaling function in a double scaling limit of the average characteristic polynomial associated with the Wilson loop operator in two dimensional QCD. We hypothesize that the transition in three and four dimensional large N QCD are also in the same universality class and provide a numerical test for our hypothesis in three dimensions.