Kaon Condensation and Goldstone’s 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 ∼ p 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 non-relativistic 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. PACS: 11.30.Rd, 12.39.Fe, 12.38.Lg, 71.30.+h