Three-flavor QCD at high density: Color-flavor locking and chiral symmetry breaking

We propose a symmetry breaking scheme for QCD with three massless quarks at high baryon density wherein the color and flavor SU(3)(color)xSU(3)(L)xSU(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 Nambu-Goldstone 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.