Spontaneous magnetization through non-Abelian vortex formation in rotating dense quark matter

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-Goldstone 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.