Numerical study of large-N phase transition of smeared Wilson loops in 4D pure YM theory

TL;DR

This paper investigates the large-N phase transition of smeared Wilson loops in 4D pure Yang-Mills theory, revealing universal critical behavior and continuum limits through lattice simulations.

Contribution

It introduces a study of smeared Wilson loop eigenvalue distributions in 4D SU(N) gauge theory, demonstrating their nontrivial continuum limit and universal critical exponents at large N.

Findings

Identification of a non-analytic phase transition at a critical loop size.

Confirmation of universal exponents 1/2 and 3/4 governing the transition.

Evidence of a well-defined continuum limit for the observable.

Abstract

In Euclidean four-dimensional SU(N) pure gauge theory, eigenvalue distributions of Wilson loop parallel transport matrices around closed spacetime curves show non-analytic behavior (a 'large-N phase transition') at a critical size of the curve. We focus mainly on an observable composed of traces of the Wilson loop operator in all totally antisymmetric representations, which is regularized with the help of smearing. By studying sequences of square Wilson loops on a hypercubic lattice with standard Wilson action, it is shown that this observable has a nontrivial continuum limit as a function of the physical size of the loop. We furthermore present (preliminary) numerical results confirming that, for large N, the N dependence in the critical regime is governed by the universal exponents 1/2 and 3/4 as expected (Burgers universality).