Hydrodynamics of the Polyakov line in SU(Nc) Yang–Mills

We discuss a hydrodynamical description of the eigenvalues of the Polyakov line at large but finite NcNc 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 NcNc, and are consistent with the string model results at Nc=∞Nc=∞. 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(Nc)Z(Nc) bubble using a piece-wise sound wave is suggested.