Positivity of QCD at asymptotic density

In this talk, I try to show that the sign problem of dense QCD is due to modes whose frequency is higher than the chemical potential. An effective theory of quasi-quarks near the Fermi surface has a positive measure in the leading order. The higher-order corrections make the measure complex, but they are suppressed as long as the chemical potential is sufficiently larger than $\Lambda_{\rm QCD}$. As a consequence of the positivity of the effective theory, we can show that the global vector symmetries except the U(1) baryon number are unbroken at asymptotic density.