Superfluids as Higher-form Anomalies

TL;DR

This paper reformulates superfluid hydrodynamics using higher-form symmetries and anomalies, providing a unified framework that encompasses phase transitions like BKT and introduces new theoretical insights.

Contribution

It introduces a novel higher-form symmetry perspective in superfluid hydrodynamics, linking anomalies to Goldstone bosons and phase transitions without relying on spontaneous symmetry breaking.

Findings

Unified hydrodynamic equations for superfluids and higher-form symmetries

Alternative proof of Goldstone bosons via Ward identities

Framework includes BKT transitions and constructs 0-form and 1-form superfluid theories

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.