Emergent higher-form symmetry in Higgs phases with superfluidity

We address emergent higher-form symmetry in Higgs phases with superfluidity. The emergent symmetry appears if a matter field is invariant under a transformation of a common subgroup of gauge and global $\mathrm{U}(1)$ symmetries. We explicitly construct the symmetry generator that is topological and gauge invariant in a low-energy effective theory. Such emergent symmetry is helpful to distinguish the Higgs and other phases with superfluidity, such as phases of QCD at finite density. We also discuss the possibility of phase transition between these phases.