An effective field theory of QCD at high density

We derive a (Wilsonian) effective field theory of QCD at finite density by integrating out the states in the Dirac sea when the chemical potential $\mu\gg\Lambda_{\rm QCD}$. The quark-gluon coupling is effectively (1+1)-dimensional and the theory contains four-quark operators which become relevant as we approach to the Fermi sea. By calculating the one-loop vacuum polarization tensor in the effective theory, we find the electric gluons have a screening mass, $M\sim g_s\mu$, while the static magnetic gluons are unscreened. We then investigate the gap equations for color anti-triplet Cooper pairs by including both gluon-exchange interactions and the marginal four-quark interactions in the effective theory.