  We study thermodynamics of free SU(N) gauge theory with a large number of
colours and flavours on a three-sphere, in the presence of a baryon number
chemical potential. Reducing the system to a holomorphic large-N matrix
integral, paying specific attention to theories with scalar flavours (squarks),
we identify novel third-order deconfining phase transitions as a function of
the chemical potential. These transitions in the complex large-N saddle point
configurations are interpreted as "melting" of baryons into (s)quarks. They are
triggered by the exponentially large (~ exp(N)) degeneracy of light baryon-like
states, which include ordinary baryons, adjoint-baryons and baryons made from
different spherical harmonics of flavour fields on the three-sphere. The phase
diagram of theories with scalar flavours terminates at a phase boundary where
baryon number diverges, representing the onset of Bose condensation of squarks.
