Field theories with higher-group symmetry from composite currents

A bstract Higher-form symmetries are associated with transformations that only act on extended objects, not point particles. Typically, higher-form live alongside ordinary, point-particle (0-form), and they can be jointly described in terms of a direct product symmetry group. However, when the actions 0-form become entangled, more general mathematical structure is required, related to higher categorical groups. Systems continuous higher-group were previously constructed top-down manner, descending from quantum field theories specific mixed ’t Hooft anomaly. I show also naturally emerges bottom-up, low-energy perspective, physical system at hand contains least two different given, spontaneously broken symmetries. This leads generically hierarchy emergent symmetries, corresponding Grassmann algebra topological currents theory, an underlying structure. Examples systems featuring such include superfluid mixtures variants axion electrodynamics.