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Hydrodynamic fluctuations and topological susceptibility in chiral magnetohydrodynamics
by Arpit Das, Nabil Iqbal, Napat Poovuttikul
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Submission summary
| Authors (as registered SciPost users): | Arpit Das · Nabil Iqbal |
| Submission information | |
|---|---|
| Preprint Link: | https://arxiv.org/abs/2403.16957v1 (pdf) |
| Date accepted: | 2024-08-06 |
| Date submitted: | 2024-05-24 08:22 |
| Submitted by: | Das, Arpit |
| Submitted to: | SciPost Physics |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
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| Approach: | Theoretical |
Abstract
Chiral magnetohydrodynamics is devoted to understanding the late-time and long-distance behavior of a system with an Adler-Bell-Jackiw anomaly at finite temperatures. The non-conservation of the axial charge is determined by the topological density $\vec{E} \cdot \vec{B}$; in a classical hydrodynamic description this decay rate can be suppressed by tuning the background magnetic field to zero. However it is in principle possible for thermal fluctuations of $\vec{E} \cdot \vec{B}$ to result in a non-conservation of the charge even at vanishing $B$-field; this would invalidate the classical hydrodynamic effective theory. We investigate this by computing the real-time susceptibility of the topological density at one-loop level in magnetohydrodynamic fluctuations, relating its low-frequency limit to the decay rate of the axial charge. We find that the frequency-dependence of this susceptibility is sufficiently soft as to leave the axial decay rate unaffected, validating the classical hydrodynamic description. We show that the susceptibility contains non-analytic frequency-dependence which is universally determined by hydrodynamic data. We comment briefly on possible connections to the recent formulation of the ABJ anomaly in terms of non-invertible symmetry.
Author indications on fulfilling journal expectations
- Provide a novel and synergetic link between different research areas.
- Open a new pathway in an existing or a new research direction, with clear potential for multi-pronged follow-up work
- Detail a groundbreaking theoretical/experimental/computational discovery
- Present a breakthrough on a previously-identified and long-standing research stumbling block
Published as SciPost Phys. 17, 042 (2024)
Reports on this Submission
Report #2 by Anonymous (Referee 2) on 2024-7-29 (Invited Report)
- Cite as: Anonymous, Report on arXiv:2403.16957v1, delivered 2024-07-29, doi: 10.21468/SciPost.Report.9488
Report
The paper sets out to perform an interesting calculation to verify the applicability of the effective low-energy long-wavelength hydrodynamic description to systems with an ABJ anomaly. The anomaly leads to a finite decay rate for the axial charge density when the magnetic field $B$ is non-zero. In the limit of zero magnetic field the axial charge becomes an exactly conserved quantity. However, the classical hydrodynamic description does not provide the full picture - there are thermal fluctuations about the state with $B = 0$ that can ruin this exact conservation, and jeopardise the applicability of the hydrodynamic description itself. To check this, the authors perform a one-loop computation involving thermal fluctuations for the axial charge decay rate, and find that it vanishes in the strict hydrodynamic limit $\omega = 0$, thereby justifying the use of hydrodynamics for such systems.
The paper is written nicely and addresses an interesting issue. I recommend it for publication in SciPost Physics.
Recommendation
Publish (meets expectations and criteria for this Journal)
Report #1 by Anonymous (Referee 1) on 2024-7-19 (Invited Report)
- Cite as: Anonymous, Report on arXiv:2403.16957v1, delivered 2024-07-19, doi: 10.21468/SciPost.Report.9434
Strengths
1- Concretely identified problem and its resolution.
2- Well-written and clearly presented.
3- Interesting albeit technical results for the target audience in the field.
Weaknesses
1- The results are quite technical in nature, but sufficient effort has been made to identify certain qualitative features.
2- The results are interesting as a consistency check for chiral magnetohydrodynamics, but do not seem to have any direct applications otherwise.
Report
The paper discusses one-loop correction to the susceptibility of topological density in chiral magnetohydrodynamics. The authors are particularly interested in the behaviour at zero magnetic field. The authors note that while classically the topological susceptibility vanishes at zero magnetic field, the same is not guaranteed to hold in the presence of loop corrections. The authors find that the one-loop corrections do indeed vanish as the magnetic field is taken to zero. This is an interesting consistency check for the validity of classical chiral magnetohydrodynamics at late times and long distances. I find the results presented in the paper quite interesting and well-presented and can recommend it for publication in SciPost Physics.
Recommendation
Publish (meets expectations and criteria for this Journal)