Deconfinement transitions of large N QCD with chemical potential at weak and strong coupling

TL;DR

This paper investigates the deconfinement phase transition lines in large N QCD with chemical potential across weak and strong coupling regimes, extending previous models and establishing consistency between continuum and lattice results.

Contribution

It extends weak-coupling matrix model results to higher temperatures and strong-coupling lattice results, providing a unified analysis of deconfinement transitions in large N QCD with chemical potential.

Findings

Deconfinement transition line extends from higher-order to third-order transition.

Weak and strong coupling results are consistent under parameter mapping at low temperatures.

Transition lines depend on temperature, chemical potential, and coupling strength.

Abstract

We calculate the deconfinement line of transitions for large Nc QCD at finite temperature and chemical potential in two different regimes: weak coupling in the continuum, and, strong coupling on the lattice, working in the limit where Nf is of order Nc. In the first regime we extend previous weak-coupling results from one-loop perturbation theory on S^1 x S^3 to higher temperatures, where the theory reduces to a matrix model, analogous to that of Gross, Witten, and Wadia. We obtain the line of transitions that extends from the temperature-axis, where to a first approximation the transition is higher than fourth order, to the chemical potential-axis, where the transition is third order. In the second regime we use the same matrix model to obtain the deconfinement line of transitions as a function of the coupling strength and mu / T to leading order in a strong coupling expansion of lattice QCD with heavy quarks, extending previous U(Nc) results to SU(Nc). We show that in the case of zero chemical potential the result obtained for the Polyakov line from QCD on S^1 x S^3 at weak coupling reproduces the known results from the strong coupling expansion, under a simple change of parameters, which is valid for sufficiently low temperatures and chemical potentials.