Quark condensation, induced symmetry breaking and color superconductivity at high density

The phase structure of hadronic matter at high density relevant to the physics of compact stars and relativistic heavy-ion collisions is studied in a low-energy effective quark theory. The relevant phases that figure are (1) chiral condensation, (2) diquark color condensation (color superconductivity) and (3) induced Lorentz-symmetry breaking ("ISB"). For a reasonable strength for the effective four-Fermi current - current interaction implied by the low-energy effective quark theory for systems with a Fermi surface we find that the "ISB" phase sets in together with chiral symmetry restoration (with the vanishing quark condensate) at a moderate density while color superconductivity associated with scalar diquark condensation is pushed up to an asymptotic density. Consequently, color superconductivity seems rather unlikely in heavy-ion collisions although it may play a role in compact stars. Lack of confinement in the model makes the result of this analysis only qualitative but the hierarchy of the transitions we find seems to be quite robust.