Kaon condensation in a Nambu-Jona-Lasinio model at high density

We demonstrate a fully self-consistent microscopic realization of a kaon-condensed color-flavor locked state (${\mathrm{CFLK}}^{0}$) within the context of a mean-field Nambu\char21{}Jona-Lasinio (NJL) model at high density. The properties of this state are shown to be consistent with the QCD low-energy effective theory once the proper gauge neutrality conditions are satisfied, and a simple matching procedure is used to compute the pion decay constant, which agrees with the perturbative QCD result. The NJL model is used to compare the energies of the ${\mathrm{CFLK}}^{0}$ state to the parity even CFL state, and to determine locations of the metal/insulator transition to a phase with gapless fermionic excitations in the presence of a nonzero hypercharge chemical potential and a nonzero strange quark mass. The transition points are compared with results derived previously via effective theories and with partially self-consistent NJL calculations. We find that the qualitative physics does not change, but that the transitions are slightly lower.