Patterns of symmetry breaking in QCD at high baryon density

Abstract

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