Topological order in the color-flavor locked phase of a ( 3 + 1 )-dimensional U ( N ) gauge-Higgs system

We study a ( 3 + 1 )-dimensional U ( N ) gauge theory with N -flavor fundamental scalar fields, whose color-flavor locked (CFL) phase has topologically stable non-Abelian vortices. The U ( 1 ) charge of the scalar fields must be N k + 1 for some integer k in order for them to be in the representation of U ( N ) gauge group. This theory has a ZN k + 1 one-form symmetry, and it is spontaneously broken in the CFL phase, i.e., the CFL phase is topologically ordered if k ≠ 0 . We also find that the world sheet of topologically stable vortices in CFL phase can generate this one-form symmetry.