  Yang-Mills theories with a gauge group SU(N_c\=3)and quark matter in the
fundamental representation share many properties with the theory of strong
interactions, QCD with N_c=3. We show that, for N_c even and in the confinement
phase, the gluonic average of the quark determinant is independent of the
boundary conditions, periodic or anti-periodic ones. We then argue that a Fermi
sphere of quarks can only exist under extreme conditions when the centre
symmetry is spontaneously broken and colour is liberated. Our findings are
supported by lattice gauge simulations for N_c=2...5 and are illustrated by
means of a simple quark model.
