Large Nc Confinement, Universal Shocks and Random Matrices

TL;DR

This paper explores the universal spectral behavior in large N_c Yang-Mills theory, linking eigenvalue dynamics to shock waves in complex Burgers equations and random matrix models, revealing deep universality and analogies with diffraction phenomena.

Contribution

It establishes a connection between eigenvalue spectral shocks in large N_c Yang-Mills theory and universal behaviors in random matrix models and diffraction catastrophes.

Findings

Eigenvalue gap closure linked to spectral shock waves.

Universal behavior explained via complex Burgers equation.

Analogies between Yang-Mills theory and diffraction catastrophes.

Abstract

We study the fluid-like dynamics of eigenvalues of the Wilson operator in the context of the order-disorder (Durhuus-Olesen) transition in large $N_c$ Yang-Mills theory. We link the universal behavior at the closure of the gap found by Narayanan and Neuberger to the phenomenon of spectral shock waves in the complex Burgers equation, where the role of viscosity is played by $1/N_c$. Next, we explain the relation between the universal behavior of eigenvalues and certain class of random matrix models. Finally, we conlude the discussion of universality by recalling exact analogies between Yang-Mills theories at large $N_c$ and the so-called diffraction catastrophes.