Color superconductivity and color–flavor locking

Lattice-gauge theory has produced unique insights and predictions for QCD at high temperature, but it has had little to say about QCD in environments rich in baryons. There are several reasons for this impasse. One of them is the fact that the fermion determinant is complex in this environment, so the standard algorithms of the subject fail. This point will be demonstrated later. Other more conventional methods, such as weak-coupling approximations, apparently apply in this environment and suggest that the theory experiences color superconductivity at asymptotically large baryon chemical potentials. There is the hope that the transition to this exotic state of matter actually occurs at a chemical potential of just a few hundred MeV. The subject of color superconductivity produces interesting conjectures for the QCD phase diagram in the T–µB plane where T is small (below a few tens of MeV) and µB is very large. In this chapter we will discuss the major points, both strengths and weaknesses, of this approach and refer the reader to the growing literature for more recent, developing events. Once lattice-gauge theory develops an algorithm that applies to this environment, these ideas will be put to stringent tests. However, for much of the rest of this chapter, we must ignore lattice-gauge theory and focus on weak-coupling methods and the BCS theory of superconductivity and its application and extensions to QCD.