Potential for the phase of the Wilson line at nonzero quark density

The contribution of quarks to the effective potential for the phase of the Wilson line is computed at nonzero temperature and quark chemical potential to one and two loop order. At zero temperature, regardless of the value of the quark chemical potential, the effective potential for the phase of the Wilson line vanishes. At nonzero temperature, for special values of the phase the free energy of quarks equals that of bosons; at nonzero chemical potential, such quarks can "Bose condense," albeit with negative density.