Quark Hadron Continuity in QCD with one Flavor

We study QCD with one flavor at finite baryon density. In the limit of very high baryon density the system is expected to be a color superconductor. In the case of one flavor, the order parameter is in a $\bar 3$ of color and has total angular momentum one. We show that in weak coupling perturbation theory, the energetically preferred phase exhibits ``color-spin-locking'', i.e. the color and spin direction of the condensate are aligned. We discuss the properties of this phase and argue that it shares important features of the hadronic phase at low density. In particular, we find an unbroken rotational symmetry, spin 3/2 quasiparticles, and an unusual mechanism for quark-anti-quark condensation. Our results are relevant to three flavor QCD in the regime where the strange quark mass is bigger than the critical value for color-flavor-locking. We find that the gaps in this case are on the order of one MeV.