Polyakov loop model with exact static quark determinant in the 't Hooft-Veneziano limit: U(N) case

TL;DR

This paper presents an exact solution to a $U(N)$ Polyakov loop model with static quark determinant, analyzing its phase diagram and phase transitions in the large $N, N_f$ limit.

Contribution

It introduces an exactly solvable deformed unitary matrix model incorporating the static determinant with explicit dependence on quark parameters.

Findings

Exact solutions for free energy, Polyakov loop expectation, and quark condensate.

Phase diagram and transition types depend on the ratio N_f/N.

Model reduces to a deformed unitary matrix model in the large N, N_f limit.

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 $\kappa =N_f/N$.