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Gauge theory for topological waves in continuum fluids with odd viscosity

by Keisuke Fujii, Yuto Ashida

Submission summary

Authors (as registered SciPost users): Keisuke Fujii
Submission information
Preprint Link: scipost_202506_00045v1  (pdf)
Date accepted: Aug. 7, 2025
Date submitted: June 24, 2025, 4:03 a.m.
Submitted by: Fujii, Keisuke
Submitted to: SciPost Physics Core
Ontological classification
Academic field: Physics
Specialties:
  • Condensed Matter Physics - Theory
  • Fluid Dynamics
  • High-Energy Physics - Theory
Approach: Theoretical

Abstract

We consider two-dimensional continuum fluids with odd viscosity under a chiral body force. The chiral body force makes the low-energy excitation spectrum of the fluids gapped, and the odd viscosity allows us to introduce the first Chern number of each energy band in the fluids. Employing a mapping between hydrodynamic variables and U(1) gauge-field strengths, we derive a U(1) gauge theory for topologically nontrivial waves. The resulting U(1) gauge theory is given by the Maxwell-Chern-Simons theory with an additional term associated with odd viscosity. We then solve the equations of motion for the gauge fields concretely in the presence of the boundary and find edge-mode solutions. We finally discuss the fate of bulk-boundary correspondence (BBC) in the context of continuum systems.

Author comments upon resubmission

In the revised manuscript, we moved the citation that was previously mentioned in the Appendix as [55] to the Introduction and now cite it as [45].
Along with this change, we revised the last paragraph of the Introduction to explicitly highlight the novelty of our results.
We also accepted the requested changes pointed out in Report #1 and revised the relevant phrasing accordingly.

List of changes

  1. We significantly revised the last paragraph of the Introduction to explicitly highlight our main new result. In that paragraph, we now cite a previous work related to the mapping to a gauge theory as Ref. [45].

  2. "As a crucial difference from solid crystals, continuum fluids lack the spatial periodicity." → "As a crucial difference from solid crystals, continuum fluids have spatial continuous periodicity."

  3. "Importantly, since the system is supposed to be in an infinitely extended bulk, its wavenumber space is given as an infinitely extended space, ..." → "Importantly, since the translational period of the system is supposed to be zero, its wavenumber space is given as an infinitely extended space."

Current status:
Accepted in target Journal

Editorial decision: For Journal SciPost Physics Core: Publish
(status: Editorial decision fixed and (if required) accepted by authors)


Reports on this Submission

Report #2 by Anonymous (Referee 1) on 2025-7-30 (Invited Report)

Report

I believe the authors have adequately addressed all the referees’ comments and made the corresponding revisions to the manuscript. I recommend accepting the manuscript for publication in SciPost Physics Core.

Recommendation

Publish (meets expectations and criteria for this Journal)

  • validity: -
  • significance: -
  • originality: -
  • clarity: -
  • formatting: -
  • grammar: -

Report #1 by Anonymous (Referee 2) on 2025-7-1 (Invited Report)

Report

My comments in my previous report stand: the paper is correct, although the translation of the well-studied Hall viscosity to the gauge theoretic formulation of the shallow water equations is not groundbreaking. Nonetheless, the paper is well-written and, in my opinion, appropriate for SciPost core.

Recommendation

Publish (meets expectations and criteria for this Journal)

  • validity: high
  • significance: ok
  • originality: ok
  • clarity: high
  • formatting: good
  • grammar: -

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