Kaon condensation and Goldstone's theorem

We consider QCD at a nonzero chemical potential for strangeness. At a criti cal value of the chemical potential equal to the kaon mass, kaon condensati on occurs through a continuous phase transition. We show that in the limit of exact isospin symmetry a Goldstone boson with the dispersion relation E similar to p(2) 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 Nie lsen and Chadha. We also formulate a criterion sufficient for the equality between the number of Goldstone bosons and the number of broken generators. (C) 2001 Published by Elsevier Science B.V.