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Superfluids as Higher-form Anomalies
by Luca V. Delacrétaz, Diego M. Hofman, Grégoire Mathys
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Submission summary
| Authors (as registered SciPost users): | Luca Delacrétaz |
| Submission information | |
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| Preprint Link: | https://arxiv.org/abs/1908.06977v2 (pdf) |
| Date accepted: | 2020-02-27 |
| Date submitted: | 2020-02-19 01:00 |
| Submitted by: | Delacrétaz, Luca |
| Submitted to: | SciPost Physics |
| Ontological classification | |
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| Academic field: | Physics |
| Specialties: |
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| Approach: | Theoretical |
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.
Author comments upon resubmission
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.
Published as SciPost Phys. 8, 047 (2020)