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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/1908.06977v1 (pdf) |
| Date submitted: | 2019-09-15 02:00 |
| 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.
Current status:
Reports on this Submission
Report #2 by Anonymous (Referee 2) on 2020-1-22 (Invited Report)
- Cite as: Anonymous, Report on arXiv:1908.06977v1, delivered 2020-01-22, doi: 10.21468/SciPost.Report.1465
Strengths
1. Elegant and systematic formulation of superfluid hydrodynamics.
2. Provide several comments with physical insights.
3. There are several potential interesting extensions.
Weaknesses
I could not find any.
Report
The paper develops a novel formalism to describe superfluid hydrodynamics in the language of generalized global symmetries and anomalies. A crucial ingredient is an emergent (d-2)-form symmetry associated with the conservation of superfluid winding planes. This symmetry has a mixed anomaly with the standard 0-form symmetry. Through a current algebra argument, the anomaly is shown to imply the existence of the Goldstone mode. The Josephson relation is stated in terms of the constitutive relation for the emergent (d-1)-form current and is naturally written in terms of a systematic derivative expansion. In transitioning to the normal fluid phase, the (d-2)-form symmetry is explicitly broken by the proliferation of vortices. The formalism can be generalized to higher-form superfluids in any dimension. As an additional example, the authors apply the formalism to QED in 4 dimensions at scales below the electron mass, which can be viewed as a 1-form superfluid. In this case, the emergent symmetry is the electric 1-form symmetry. The paper has a clear structure and contains results which can lead to further investigation on this topic. I therefore recommend the paper for publication.
Requested changes
None.
Report #1 by Anonymous (Referee 1) on 2019-10-15 (Invited Report)
- Cite as: Anonymous, Report on arXiv:1908.06977v1, delivered 2019-10-15, doi: 10.21468/SciPost.Report.1224
Strengths
1. new perspective on superfluid hydrodynamics from higher-form symmetries
2. mixed anomalies involving higher-form symmetries predict/protect certain massless modes in the EFT (such as the goldstone field in superfluid)
3. streamlined understanding of the usual hydrodynamic equations by including higher-form symmetry currents
Weaknesses
See requested changes
Report
The authors provide a new perspective on conventional superfluid hydrodynamics by identifying an emergent higher-form symmetry in the EFT: a (d-2)-from symmetry, and analyzing its implications. In particular, due to a mixed anomaly with the ordinary U(1) 0-form symmetry, they explained nicely using just the correlators of the conserved currents that a goldstone mode for the U(1) 0-form symmetry must be present (without assuming SSB). They went on to show that by incorporating (anomalous) conservation and constituent relations for the higher form symmetry, one recover the usual hydrodynamic equations for the ordinary superfluid in an elegant and uniform fashion. They also discussed the 1-form superfluid case which is relevant for the low energy phase of 4d QED. The paper is well-structured and nicely-written. It presents a fruitful dialogue between generalized symmetries, anomalies and hydrodynamics. I recommend this paper for publication.
Requested changes
The current as written in (1.3) is not conserved. The actual (d-1)-form current is *d\phi. But this is not invariant under the 0-from U(1) gauge transformation. What the authors wrote is the gauge invariant improvement whose non-conservation leads to the anomaly. It maybe worthwhile to explain this.