Universal properties of Wilson loop operators in large N QCD

TL;DR

This paper investigates the universal behavior of Wilson loop eigenvalue distributions in large N QCD, deriving a scaling function in 2D and providing numerical evidence for similar transitions in 3D and 4D.

Contribution

It introduces a universal scaling function for Wilson loop eigenvalues in large N QCD and hypothesizes the universality class extends to higher dimensions.

Findings

Derived the scaling function in 2D QCD

Provided numerical evidence for similar transitions in 3D QCD

Suggested universality class for Wilson loop eigenvalue transitions

Abstract

Eigenvalues of a Wilson loop operator are gauge invariant and their distribution undergoes a transition at infinite N as the size of the loop is changed. We study this transition using the average characteristic polynomial associated with the Wilson loop operator. We derive the scaling function in a certain double scaling limit for two dimensional QCD and hypothesize that the transition in three and four dimensional QCD are in the same universality class. Numerical evidence for this hypothesisis provided in three dimensions