Stable non-Abelian semi-superfluid vortices in high density QCD

Color superconductivity is expected to be formed in high density quark matter where `color symmetry' is `spontaneously broken' in the presence of di-quark condensate. Stable non-Abelian vortices or color magnetic flux tubes exist in the color-flavor locked phase at asymptotically high density. CP2 Nambu- Goldstone(NG) bosons and Majorana fermions belonging to the triplet representation are localized around a non-Abelian vortex. In this seminar I would like to discuss the construction of single non-Abelian vortex solution and its zero modes. The low-energy effective world sheet theory of a non-Abelian vortex would be discussed briefly where the interactions of these bosonic and fermionic modes would be written down by using the nonlinear realization method. We discuss the Aharanov-Bohm (AB) phases of charged particles, such as, electrons, muons, and color-flavor locked mesons made of tetra-quarks encircling around a non-Abelian vortex in the presence of electro-magnetic fields. The hadron-quark continuity would be discussed briefly in the presence of vortices. Finally I would like to touch upon a possible duality between zero density QCD and CFL phase.