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

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## Abstract

We calculate the deconfinement line of transitions for large *N* _{ c } 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 *N* _{ f } is of order *N* _{ c }. In the first regime we extend previous weak-coupling results from one-loop perturbation theory on *S* ^{1} × *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 *μ*/*T* to leading order in a strong coupling expansion of lattice QCD with heavy quarks, extending previous U(*N* _{ c }) results to SU(*N* _{ c }). We show that in the case of zero chemical potential the result obtained for the Polyakov line from QCD on *S* ^{1} × *S* ^{3} at weak coupling reproduces the known results from the lattice strong coupling expansion, under a simple change of parameters, which is valid for sufficiently low temperatures and chemical potentials.

## Keywords

1/N Expansion Phase Diagram of QCD## References

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