Hydrodynamics of the Polyakov Line in SU$(N_c)$ Yang-Mills

TL;DR

This paper develops a hydrodynamical framework to describe the eigenvalue distributions of the Polyakov line in SU(N_c) Yang-Mills theory, connecting phase transitions with lattice and string model results.

Contribution

It introduces a hydrodynamical model for Polyakov line eigenvalues at finite N_c, capturing phase transitions and out-of-equilibrium dynamics in Yang-Mills theory.

Findings

Hydro-static solutions interpolate between confined and deconfined phases.

Critical temperatures align with lattice measurements across N_c.

Hydrodynamical instantons describe stochastic relaxation processes.

Abstract

We discuss a hydrodynamical description of the eigenvalues of the Polyakov line at large but finite $N_c$ for Yang-Mills theory in even and odd space-time dimensions. The hydro-static solutions for the eigenvalue densities are shown to interpolate between a uniform distribution in the confined phase and a localized distribution in the de-confined phase. The resulting critical temperatures are in overall agreement with those measured on the lattice over a broad range of $N_c$, and are consistent with the string model results at $N_c=\infty$. The stochastic relaxation of the eigenvalues of the Polyakov line out of equilibrium is captured by a hydrodynamical instanton. An estimate of the probability of formation of a Z(N$_c)$ bubble using a piece-wise sound wave is suggested.