Confinement, Turbulence and Diffraction Catastrophes

TL;DR

This paper explores the connection between spectral transitions in Wilson loops of Yang-Mills theory and turbulence modeling, revealing universal scaling laws linked to diffraction catastrophes.

Contribution

It introduces a Burgers equation framework to model spectral shocks in Wilson loops, connecting turbulence, diffraction catastrophes, and large N_c transitions.

Findings

Spectral shock waves exhibit universal N_c scaling.

Indices relate to Berry indices for diffraction catastrophes.

Model captures features observed in numerical Yang-Mills simulations.

Abstract

Many features of large N_c transition that occurs in the spectral density of Wilson loops as a function of loop area (observed recently in numerical simulations of Yang-Mills theory by Narayanan and Neuberger) can be captured by a simple Burgers equation used to model turbulence. Spectral shock waves that precede this asymptotic limit exhibit universal scaling with N_c, with indices that can be related to Berry indices for diffraction catastrophes.