Universal properties of large N phase transitions in Wilson loops

TL;DR

This paper discusses a conjecture that Wilson loop eigenvalue densities in continuum planar QCD undergo a universal phase transition as the loop size increases, consistent across multiple dimensions, supported by numerical evidence.

Contribution

It clarifies the precise nature of the conjecture regarding large N universality of phase transitions in Wilson loops across different dimensions.

Findings

Eigenvalue density transition supports large N universality

Transition behavior is consistent in 2, 3, and 4 dimensions

Numerical studies back the conjecture

Abstract

Numerical studies support the conjecture that in continuum planar QCD the eigenvalue density of a Wilson loop operator undergoes a transition as the loop is dilated while keeping the loop shape fixed. A second part of the conjecture is that the transition obeys large N universality and that this universality class is the same in 2, 3 and 4 Euclidean space-time dimensions. The focus of the talk will be on clarifying precisely what the conjecture is claiming.