Diquark Condensation in High Density Baryon Matter

Over the past years, important progress has been achieved in our understanding of the phase structure of QCD at finite temperature. Even though many important points remain to be worked out (like the nature of the QCD phase transition for realistic values of the quark masses), there is a nice frame work based on universality arguments and our ability to perform simulations on the lattice. For reasons that we do not need to reiterate here, the problem of cold dense matter is much less understood. On the other hand, it has been realized for quite some time that the possible phase structure of dense matter is very rich. In addition to the nuclear and quark matter phases, new phases containing pion or kaon condensates, strange quark matter, etc., have been suggested. In this contribution we want to study the possibility that cold quark matter is in a superconducting phase. The Cooper pairs of QCD are spin zero diquarks. Unlike many of the phases that we just mentioned, this phenomenon is very robust and independent of the detailed dynamics. It is based on the observation that a sharp Fermi surface is expected to be unstable with respect to pair condensation whenever there is an (arbitrarily weak!) attractive interaction between quarks pairs in the vicinity of the Fermi surface.