  When a color superconductor of high density QCD is rotating, superfluid
vortices are inevitably created along the rotation axis. In the color-flavor
locked phase realized at the asymptotically large chemical potential, there
appear non-Abelian vortices carrying both circulations of superfluid and color
magnetic fluxes. A family of solutions has a degeneracy characterized by the
Nambu-Goldtone modes CP2, associated with the color-flavor locked symmetry
spontaneously broken in the vicinity of the vortex. In this paper, we study
electromagnetic coupling of the non-Abelian vortices and find that the
degeneracy is removed with the induced effective potential. We obtain one
stable vortex solution and a family of metastable vortex solutions, both of
which carry ordinary magnetic fluxes in addition to color magnetic fluxes. We
discuss quantum mechanical decay of the metastable vortices by quantum
tunneling, and compare the effective potential with the other known potentials,
the quantum mechanically induced potential and the potential induced by the
strange quark mass.
