A Random Matrix Model for Color Superconductivity at Zero Chemical Potential

We discuss random matrix models for the spontaneous breaking of both chiral and color symmetries at zero chemical potential and finite temperature. Exploring different Lorentz and gauge symmetric color structures of the random matrix interactions, we find that spontaneous chiral symmetry breaking is always thermodynamically preferred over diquark condensation. Stable diquark condensates appear only as SU(2) rotated chiral condensates, which do not represent an independent thermodynamic phase. Our analysis is based on general symmetry arguments and hence suggests that no stable and independent diquark phase can form in QCD with two flavors at zero quark chemical potential.