Baryons and the phase diagram for a large number of colors and flavors

We consider the possible phases of a non-Abelian gauge theory, as a function of temperature and quark chemical potential, when both the number of colors and flavors is very large. Generally, a large number of flavors washes out deconfining phase transitions. We show, however, that the degeneracy of even the lightest baryons is exponentially large. This implies that the baryon number (or fluctuations thereof, at zero chemical potential) is an order parameter in the limit of an infinite number of colors and flavors.