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 $N_f$. 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 $SU(3)_L\times SU(3)_R\to SU(3)$, 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 $<\bar\psi\psi>$ and $<(\bar\psi\psi)^2>$ in perturbative QCD. We show that, asymptotically, $<\bar\psi\psi>^{1/3}$ is much smaller than $<(\bar\psi\psi)^2>^{1/6}$. The result can be understood in terms of an approximate discrete symmetry.