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

In this note we summarize the results from a longer article on obtaining the QCD phase diagram as a function of the temperature and chemical potential at large Nc and large Nf in the weak and the strong coupling limits. The weak coupling phase diagram is obtained from the Polyakov line order parameter, and the quark number, calculated using 1-loop perturbation theory for QCD formulated on S^1 x S^3. The strong coupling phase diagram is obtained from the same observables calculated at leading order in the lattice strong coupling and hopping parameter expansions. We show that the matrix models in these two limits agree at temperatures and chemical potentials which are not too high, such that observables in the strongly-coupled theory can be obtained from the observables in the weakly-coupled theory, and vice versa, using a simple transformation of variables.