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

QCD at non-zero chemical potential provides a description of systems with a quark-antiquark asymmetry, yet it is a description which is currently not directly accessible since it occurs at strong coupling and the non-zero chemical potential leads to a complex action, giving rise to the well-known sign problem. What this means is that the conventional techniques of studying finite temperature QCD: conventional lattice simulations and ordinary perturbation theory, are not applicable. In this talk we consider two nonconventional perturbative techniques which allow us to calculate the partition function and related observables such as the Polyakov line deconfinement order parameter and quark number, and from these to map out the phase diagram for an otherwise inaccessible range of temperatures and chemical potentials. We calculate the QCD phase diagram at large Nc and large Nf as a function of the temperature and chemical potential in the weak coupling and strong coupling limits. At weak coupling the relevant observables are calculated using 1-loop perturbation theory for QCD formulated on S^1 x S^3. At strong coupling the calculations are performed 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.