Superfluids as Higher-form Anomalies

TL;DR

This work recasts superfluid hydrodynamics as the hydrodynamics of a system with an emergent $U(1) imes U(1)^{(d-2)}$ symmetry and a mixed anomaly. By deriving zeroth- and first-order hydrodynamics for both 0-form and 1-form cases, it shows that anomaly data fixes key transport structures and reveals a massless mode as a consequence of the anomaly rather than explicit symmetry breaking. The formalism unifies Josephson-type relations with higher-form current conservation and extends naturally to higher-form fluids, including a concrete 1-form example in four dimensions with a background two-form field. It also clarifies how phase relaxation due to vortices can be viewed as explicit breaking of higher-form symmetry and situates BKT and related transitions within a generalized symmetry framework. The results offer a broad, symmetry-based lens for classifying gapless phases and connect to holography, topological phases, and potential non-Abelian generalizations.

Abstract

We recast superfluid hydrodynamics as the hydrodynamic theory of a system with an emergent anomalous higher-form symmetry. The higher-form charge counts the winding planes of the superfluid -- its constitutive relation replaces the Josephson relation of conventional superfluid hydrodynamics. This formulation puts all hydrodynamic equations on equal footing. The anomalous Ward identity can be used as an alternative starting point to prove the existence of a Goldstone boson, without reference to spontaneous symmetry breaking. This provides an alternative characterization of Landau phase transitions in terms of higher-form symmetries and their anomalies instead of how the symmetries are realized. This treatment is more general and, in particular, includes the case of BKT transitions. As an application of this formalism we construct the hydrodynamic theories of conventional (0-form) and 1-form superfluids.