Confinement and the quark Fermi surface in SU(2N) QCD-like theories

Yang-Mills theories with a gauge group SU(N-c not equal 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 antiperiodic ones. We then argue that a Fermi sphere of quarks can only exist under extreme conditions when the center symmetry is spontaneously broken and color 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.