Fermion structure of non-Abelian vortices in high density QCD

We study the internal structure of a non-Abelian vortex in color superconductivity with respect to quark degrees of freedom. Stable non-Abelian vortices appear in the color-flavor-locked phase whose symmetry SU(3)c+L+R is further broken to SU(2)c+L+R-U(1)c+L+R at the vortex cores. Microscopic structure of vortices at scales shorter than the coherence length can be analyzed by the Bogoliubov-de Gennes equation (rather than the Ginzburg-Landau equation). We obtain quark spectra from the Bogoliubov-de Gennes equation by treating the diquark gap having the vortex configuration as a background field. We find that there are massless modes (zero modes) well-localized around a vortex, in the triplet and singlet states of the unbroken symmetry SU(2)c+L+R-U(1)c+L+R. The velocities vi of the massless modes (i=t, s for triplet and singlet) change at finite chemical potential μ 0, and decrease as μ becomes large. Therefore, low energy excitations in the vicinity of the vortices are effectively described by 1+1 dimensional massless fermions whose velocities are reduced vi<1.