Patterns of symmetry breaking in QCD at high baryon density

We study the structure of QCD at very large baryon density for an arbitrary number of flavors Nf. We provide evidence that for any number of flavors larger than Nf=2 chiral symmetry remains broken at asymptotically large chemical potential. For Nc=Nf=3, chiral symmetry breaking follows the standard pattern SU(3)LxSU(3)R→SU(3), but for Nf>3 unusual patterns emerge. We study the case Nf=3 in more detail and calculate the magnitude of the chiral order parameters <ψ-barψ> and <(ψ-barψ)2> in perturbative QCD. We show that, asymptotically, <ψ-barψ>1/3 is much smaller than <(ψ-barψ)2>1/6. The result can be understood in terms of an approximate discrete symmetry