  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.
