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 Nk+1 for some integer k in order for them to be in the representation of U(N) gauge group. This theory has a ZNk+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.