Dispersion laws for Goldstone bosons in a color superconductor

The effective action for Goldstone bosons in the color-flavor locking phase of dense QCD is analyzed. Interaction terms and higher derivatives in the effective action appear to be controlled by different scales. At energies of order of the superconducting gap, the derivative expansion breaks down, while interactions still remain suppressed. The effective action valid at energies and momenta comparable to the gap is derived. Dispersion laws following from this action are such that the energy of Goldstone bosons is always smaller than the gap in the quasiparticle spectrum, and Goldstone bosons always propagate without damping.