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At very high densities, QCD is in the color-flavor locked phase, which is acolor-superconducting phase. The diquark condensates break chiral symmetry inthe same way as it is broken in vacuum QCD and gives rise to an octet ofpseudo-Goldstone bosons and a superfluid mode. The lightest of these are thecharged and neutral kaons. For energies below the superconducting gap, thekaons are described by an $O(2)\times O(2)$-symmetric effective scalar fieldtheory with chemical potentials. We use this effective theory to studyBose-condensation of kaons and their properties as functions of the temperatureand the chemical potentials. We use the 2-particle irreducible effective actionformalism in the Hartree approximation. The renormalization of the gapequations and the effective potential is studied in detail and we show that thecounterterms are independent of temperature and chemical potentials.Wedetermine the phase diagram and the medium-dependent quasiparticle masses. Itis shown that the Goldstone theorem is satisfied to a very goodapproximation.The effects of imposing electric charge neutrality is examined as well.

Kaon condensation in the color-flavor-locked phase of quark matter, the Goldstone theorem, and the 2PI Hartree approximation