We find chiral non-Abelian vortices having windings only in one of the diquark condensations of left-handed and right-handed quarks in the color-flavor locked phase of dense QCD. They are the minimum vortices carrying half color magnetic fluxes of those of non-Abelian semisuperfluid vortices (color magnetic flux tubes) and 1/6 quantized superfluid circulations of Abelian superfluid vortices. These vortices carry CP2 orientational moduli in the internal space corresponding to their fluxes. The CP2 moduli of two chiral non-Abelian vortices with chiralities opposite to each other are energetically favored to be aligned while those of a vortex and antivortex to be orthogonal, and then these vortices attract each other. They are attached by chiral domain walls in the presence of the mass and axial anomaly terms explicitly breaking axial and chiral symmetries. We numerically show that two chiral non-Abelian vortices with chiralities opposite to each other are connected by a chiral domain wall, consisting a mesonic bound state which is nothing but a non-Abelian semisuperfluid vortex. We also show that Abelian and non-Abelian axial vortices attached by chiral domain walls are all unstable to decay into a set of chiral non-Abelian vortices. Furthermore, we find that chiral non-Abelian vortices exhibit unique features: One is the so-called topological obstruction implying that unbroken symmetry generators in the bulk are not defined globally around the vortices, and the other is color nonsinglet Aharonov-Bohm (AB) phases implying that quarks encircling these vortices can detect the colors of magnetic fluxes of them at infinite distances.
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