Polyakov loop model with exact static quark determinant in the 't Hooft-Veneziano limit: U(N) case
S. Voloshyn
TL;DR
The work develops and solves a Polyakov-loop model incorporating the exact static quark determinant in the 't Hooft–Veneziano limit, where mean-field theory becomes exact. By reducing the core to a deformed unitary matrix model, the authors derive the free energy, the Polyakov-loop expectation value, and the quark condensate, and map the phase structure as a function of the quark-to-color ratio $ appa = N_f/N$. They identify a third-order Gross–Witten–Wadia–type transition that persists for general parameter sets, with a first-order switch when $ appa o 0$ or $g_+ eq g_-$. The results provide exact analytic control over observables in a strongly coupled, finite-density regime and lay groundwork for extensions to $SU(N)$ with baryon density.
Abstract
I investigate a $d$-dimensional $U(N)$ Polyakov loop model that includes the exact static determinant with $N_f$ degenerate quark flavor and depends explicitly on the quark mass and chemical potential. In the large $N, N_f$ limit mean field gives the exact solution, and the core of the Polyakov loop model is reduced to a deformed unitary matrix model, which I solve exactly. I compute the free energy, the expectation value of the Polyakov loop, and the quark condensate. The phase diagram of the model and the type of phase transition is investigated and shows it depends on the ratio $κ=N_f/N$.