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} x 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 (B-dG) equation (rather than the Ginzburg-Landau equation). We obtain quark spectra from the B-dG 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} x U(1)_{c+L+R}. The velocities v_i of the massless modes (i=t,s for triplet and singlet) change at finite chemical potential \mu, and decrease as \mu 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 v_i<1.