ar X iv : h ep - p h / 98 07 31 8 v 1 9 J ul 1 99 8 1 Three - Flavor QCD at High Density : Color - Flavor Locking and Chiral

We propose a symmetry breaking scheme for QCD with three massless quarks at high baryon density wherein the color and flavor SU(3)color×SU(3)L×SU(3)R symmetries are broken down to the diagonal subgroup SU(3)color+L+R by the formation of a condensate of quark Cooper pairs. We discuss general properties that follow from this hypothesis, including the existence of gaps for quark and gluon excitations, the existence of NambuGoldstone bosons which are excitations of the diquark condensate, and the existence of a modified electromagnetic gauge interaction which is unbroken and which assigns integral charge to the elementary excitations. We present mean-field results for a Hamiltonian in which the interaction between quarks is modelled by that induced by single-gluon exchange. We find gaps of order 10-100 MeV for plausible values of the coupling. We discuss the effects of nonzero temperature, nonzero quark masses and instanton-induced interactions on our results.