Kaon condensation and Goldstoneʹs theorem

We consider QCD at a nonzero chemical potential for strangeness. At a critical value of the chemical potential equal to the kaon mass, kaon condensation occurs through a continuous phase transition. We show that in the limit of exact isospin symmetry a Goldstone boson with the dispersion relation E∼p2 appears in the kaon condensed phase. At the same time, the number of the Goldstone bosons is less than the number of broken generators. Both phenomena are familiar in nonrelativistic systems. We interpret our results in terms of a Goldstone boson counting rule found previously by Nielsen and Chadha. We also formulate a criterion sufficient for the equality between the number of Goldstone bosons and the number of broken generators.