Goldstone boson counting in linear sigma models with chemical potential

Abstract

We analyze the effects of finite chemical potential on spontaneous breaking of internal symmetries within the class of relativistic field theories described by the linear sigma model. Special attention is paid to the emergence of ``abnormal'' Goldstone bosons with a quadratic dispersion relation. We show that their presence is tightly connected to nonzero density of the Noether charges, and formulate a general counting rule. The general results are demonstrated on an $\mathrm{SU}(3)\ifmmode\times\else\texttimes\fi{}\mathrm{U}(1)$ invariant model with an SU(3)-sextet scalar field, which describes one of the color-superconducting phases of QCD.