Carlson-Goldman modes in the color superconducting phase of dense QCD

We predict the existence of the gapless Carlson-Goldman modes in the color-flavor locked color superconducting phase of dense QCD. These modes resemble Nambu-Goldstone modes of the superconducting phase below the critical temperature where the Anderson-Higgs mechanism takes place. These modes exist in the broken phase in the vicinity of the critical line. Their presence does not eliminate the Meissner effect. The effect of Landau damping on the width of the Carlson-Goldman modes is discussed.Comment: 5 pages, 2 figures. A few new formulas and references are added, some numerical errors are corrected, and Fig. 1 is replaced by a new one. To appear in Phys. Rev.