Large Nc Confinement, Universal Shocks and Random Matrices

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.