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Higher-form symmetries, anomalous magnetohydrodynamics, and holography

by Arpit Das, Ruth Gregory, Nabil Iqbal

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Submission summary

Authors (as registered SciPost users): Arpit Das · Nabil Iqbal
Submission information
Preprint Link: scipost_202211_00028v1  (pdf)
Date accepted: 2023-04-12
Date submitted: 2022-11-16 15:40
Submitted by: Das, Arpit
Submitted to: SciPost Physics
Ontological classification
Academic field: Physics
  • Condensed Matter Physics - Theory
  • High-Energy Physics - Theory


In $U(1)$ Abelian gauge theory coupled to fermions, the non-conservation of the axial current due to the chiral anomaly is given by a dynamical operator $F_{\mu\nu} \tilde{F}^{\mu\nu}$ constructed from the field-strength tensor. We attempt to describe this physics in a universal manner by casting this operator in terms of the 2-form current for the 1-form symmetry associated with magnetic flux conservation. We construct a holographic dual with this symmetry breaking pattern and study some aspects of finite temperature anomalous magnetohydrodynamics. We explicitly calculate the charge susceptibility and the axial charge relaxation rate as a function of temperature and magnetic field and compare to recent lattice results. At small magnetic fields we find agreement with elementary hydrodynamics weakly coupled to an electrodynamic sector, but we find deviations at larger fields.

Published as SciPost Phys. 14, 163 (2023)

Author comments upon resubmission

We have replied to the referees in the Reply to a Report page and hence we do not repeat our replies here.

List of changes

List of changes:

1. Added footnote [2] on page 8 commenting on the bulk holographic action in Eq.(3.2)

2. Changed the definition of susceptibility in Eq.(4.3) and added how susceptibility is related to the chiral chemical potential in the linear regime in Eq.(4.4)

3. Added a paragraph above Numerical Results’ section explaining issues related to back-reaction and 1/N effects which we elaborate upon in the report

4. Added footnote [14] below Eq.(7.1) to comment on the scenario where the relaxation rate may not vanish even if the magnetic field vanishes. We elaborate upon this further in the report.

Reports on this Submission

Report 1 by Luca Delacrétaz on 2022-11-22 (Invited Report)

  • Cite as: Luca Delacrétaz, Report on arXiv:scipost_202211_00028v1, delivered 2022-11-22, doi: 10.21468/SciPost.Report.6176


The authors have addressed my questions.

A loophole remain concerning the longevity of the axial current, which they argue for in their reply:

"[...] this analysis appears to show that at small magnetic fields the decay rate vanishes as B^2 (where B is the magnetic field). If this is correct, it can indeed be made parametrically small, and one might seek a universal description that works at least in this regime"

However they also acknowledge that there could be a universal B independent contribution to $\Gamma_A$ coming from hydrodynamic fluctuations. I agree with the authors that this contribution may turn out to vanish ("It also seems possible that the appropriate low-frequency correlator always vanishes due to special properties of the topological density"), but it would be nice to confirm this with the explicit calculation. I leave it to the authors whether they prefer to include this calculation in this paper or save it for future work.

I recommend this paper for publication.

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