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Superfluids as Higher-form Anomalies

by Luca V. Delacrétaz, Diego M. Hofman, Grégoire Mathys

Submission summary

As Contributors: Luca Delacrétaz
Arxiv Link:
Date accepted: 2020-02-27
Date submitted: 2020-02-19
Submitted by: Delacrétaz, Luca
Submitted to: SciPost Physics
Discipline: Physics
Subject area: High-Energy Physics - Theory
Approach: Theoretical


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.

Ontology / Topics

See full Ontology or Topics database.

Anomalies Hydrodynamics Landau levels Superfluidity

Published as SciPost Phys. 8, 047 (2020)

Author comments upon resubmission

We thank both referees for their positive feedback, and referee 1 for their suggested change. We clarified this point in footnote 2.

List of changes

- Added footnote 2, explaining that the conserved (d-1)-form current is *d\phi, but is not gauge invariant.

- Sharpened Eq. (1.24), which now not only shows that the currents are not aligned, but also provides an expression for the normal density of a relativistic superfluid at low temperatures.

Submission & Refereeing History

Resubmission 1908.06977v2 on 19 February 2020
Submission 1908.06977v1 on 15 September 2019

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