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When a color superconductor of high density QCD is rotating, superfluidvortices are inevitably created along the rotation axis. In the color-flavorlocked phase realized at the asymptotically large chemical potential, thereappear non-Abelian vortices carrying both circulations of superfluid and colormagnetic fluxes. A family of solutions has a degeneracy characterized by theNambu-Goldtone modes CP2, associated with the color-flavor locked symmetryspontaneously broken in the vicinity of the vortex. In this paper, we studyelectromagnetic coupling of the non-Abelian vortices and find that thedegeneracy is removed with the induced effective potential. We obtain onestable vortex solution and a family of metastable vortex solutions, both ofwhich carry ordinary magnetic fluxes in addition to color magnetic fluxes. Wediscuss quantum mechanical decay of the metastable vortices by quantumtunneling, and compare the effective potential with the other known potentials,the quantum mechanically induced potential and the potential induced by thestrange quark mass.

Spontaneous Magnetization through Non-Abelian Vortex Formation in Rotating Dense Quark Matter