arxiv: 2604.23849 · v1 · submitted 2026-04-26 · ✦ hep-th · hep-ph· nucl-th

Recognition: unknown

Weyl anomaly induced transport in hydrodynamics

Shi-Zheng Yang , Jian-Hua Gao , Zuo-Tang Liang , Georgy Yu. Prokhorov , Shi Pu , Oleg V. Teryaev , Valentin I. Zakharov

Authors on Pith no claims yet

Pith reviewed 2026-05-08 05:40 UTC · model grok-4.3

classification ✦ hep-th hep-phnucl-th

keywords Weyl anomalytrace anomalyrelativistic hydrodynamicsanomaly-induced transportsecond-order transportaccelerated fluidsRindler horizonnon-dissipative current

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The pith

The Weyl trace anomaly produces a new non-dissipative vector current in accelerated relativistic fluids by fixing a second-order transport coefficient for electromagnetic coupling to acceleration.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

This paper shows that the Weyl or trace anomaly in conformal field theories generates an additional vector current when relativistic fluids accelerate. The current is non-dissipative and stems from how electromagnetic fields couple to the fluid acceleration at second order in the hydrodynamic expansion. The authors extend the usual anomaly-matching procedure in hydrodynamics to incorporate the trace anomaly and confirm the result independently by modeling the Rindler horizon of an accelerated observer as a boundary in quantum field theory. A reader would care because the result identifies a new mechanism for producing charge densities and transverse currents without dissipation, distinct from chiral anomalies.

Core claim

The Weyl (trace) anomaly gives rise to a new non-dissipative vector current in accelerated relativistic fluids. The anomaly uniquely fixes the second-order transport coefficient governing the coupling between the electromagnetic field and the fluid acceleration. This is derived by extending hydrodynamic anomaly matching to include the trace anomaly and reproduced by treating the Rindler horizon of an accelerated observer as an effective boundary, where the electric- and magnetic-field sectors correspond to screening and vacuum magnetization effects near the boundary.

What carries the argument

The extension of hydrodynamic anomaly matching to the trace anomaly, which determines the transport coefficient for the coupling of electromagnetic fields to fluid acceleration.

If this is right

In the local rest frame the electric-field contribution induces an additional charge density.
The magnetic-field contribution generates a transverse current with a Nernst-like, more generally thermomagnetic Hall-like, tensor structure.
The transport is non-dissipative and belongs to a new class of anomaly-induced effects governed by the trace anomaly.
The coefficient is uniquely determined with no free parameters at second order.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

The boundary calculation implies that horizon-like effects can constrain flat-space transport coefficients even when curvature is absent.
The result provides a consistency check for hydrodynamic descriptions of systems where acceleration and electromagnetic fields coexist.
Extensions to non-conformal fluids would require additional coefficients that the pure trace anomaly cannot fix.

Load-bearing premise

The standard hydrodynamic anomaly-matching procedure can be extended to the trace anomaly without introducing new undetermined coefficients or violating consistency conditions, and the Rindler-horizon boundary treatment faithfully reproduces the local transport in flat-space accelerated frames.

What would settle it

A measurement or numerical simulation of the induced charge density from an electric field or the transverse current from a magnetic field in an accelerated relativistic fluid, checking whether the magnitude matches the coefficient fixed solely by the Weyl anomaly.

Figures

Figures reproduced from arXiv: 2604.23849 by Georgy Yu. Prokhorov, Jian-Hua Gao, Oleg V. Teryaev, Shi Pu, Shi-Zheng Yang, Valentin I. Zakharov, Zuo-Tang Liang.

**Figure 1.** Figure 1: FIG. 1. Illustration of the Weyl-anomaly-induced current in view at source ↗

**Figure 2.** Figure 2: FIG. 2. Illustration of the Weyl-anomaly-induced current in view at source ↗

read the original abstract

We show that the Weyl (trace) anomaly gives rise to a new non-dissipative vector current in accelerated relativistic fluids. The anomaly uniquely fixes the second-order transport coefficient governing the coupling between the electromagnetic field and the fluid acceleration. We derive this result by extending hydrodynamic anomaly matching to include the trace anomaly, and independently reproduce it in boundary quantum field theory by treating the Rindler horizon of an accelerated observer as an effective boundary. From the boundary perspective, the electric- and magnetic-field sectors correspond to screening and vacuum magnetization effects near the boundary. In the local rest frame, the electric-field contribution induces an additional charge density, while the magnetic-field contribution generates a transverse current with a Nernst-like, more generally thermomagnetic Hall-like, tensor structure. Our results reveal a new class of anomaly-induced transport governed by the trace anomaly.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

The paper derives a new trace-anomaly fixed current in accelerated hydrodynamics via two routes, but the Rindler boundary step risks non-local contamination.

read the letter

The central result is a new non-dissipative vector current in relativistic fluids whose coefficient is fixed by the Weyl trace anomaly. The authors extend standard hydrodynamic anomaly matching to the trace anomaly and obtain a unique second-order term coupling the electromagnetic field to fluid acceleration. They then reproduce the identical coefficient from a boundary QFT calculation that treats the Rindler horizon of an accelerated observer as an effective boundary, with electric fields producing extra charge density and magnetic fields producing a transverse current of Nernst-like form. Both methods agreeing on the same expression is the clearest strength here; prior anomaly transport work has largely stayed with chiral anomalies, so this is a concrete addition inside the existing framework. The local rest-frame expressions are written out explicitly enough to be usable by people doing heavy-ion or early-universe hydro. The soft spot is the Rindler construction. The horizon carries global Unruh temperature, entanglement, and redshift factors whose contributions are not automatically guaranteed to vanish in the strict local hydrodynamic limit. If any residual non-local piece survives, the coefficient is no longer purely fixed by the local trace anomaly. The abstract and the stress-test note give no explicit check that those pieces drop out, so the locality claim rests on an assumption that still needs verification. This work is for specialists already using second-order relativistic hydrodynamics with anomalies. A reader who needs the full set of transport coefficients for accelerated fluids will find a new term worth testing. It is coherent on its own terms and shows clear engagement with the literature, so it deserves a serious referee who can press on the locality issue in the boundary calculation. I would send it to review rather than desk-reject.

Referee Report

2 major / 1 minor

Summary. The paper claims that the Weyl (trace) anomaly induces a new non-dissipative vector current in accelerated relativistic fluids. The anomaly uniquely fixes the second-order transport coefficient for the coupling between the electromagnetic field and fluid acceleration. This is obtained by extending hydrodynamic anomaly matching to the trace anomaly and independently reproduced in a boundary QFT calculation by treating the Rindler horizon as an effective boundary. In the local rest frame, the electric-field sector induces additional charge density while the magnetic-field sector generates a transverse current with Nernst-like (thermomagnetic Hall) tensor structure.

Significance. If the result holds, the work identifies a new class of anomaly-induced transport governed by the trace anomaly (rather than chiral anomalies), with possible relevance to accelerated relativistic fluids in heavy-ion collisions or astrophysical settings. The dual derivation via anomaly matching and boundary QFT is a strength, as is the claim that the coefficient is fixed without new free parameters. The physical interpretation in terms of screening and vacuum magnetization near the boundary is useful.

major comments (2)

[§3] §3 (hydrodynamic anomaly matching): The central claim that the trace-anomaly extension fixes the second-order coefficient without new undetermined parameters or consistency violations requires the explicit constitutive relation for the vector current and the precise matching condition (e.g., the relevant Ward identity or conservation equation) that determines the coefficient. Without this, the uniqueness cannot be verified from the text.
[§4] §4 (Rindler boundary QFT): The boundary construction reproduces the same local coefficient. The manuscript must explicitly demonstrate that non-local horizon contributions (Unruh temperature, redshift factors, entanglement entropy) decouple in the local hydrodynamic limit of flat-space accelerated frames; otherwise the agreement with the anomaly-matching result does not establish that the coefficient is purely local and trace-anomaly fixed.

minor comments (1)

[Abstract and §2] The abstract and introduction refer to a 'Nernst-like, more generally thermomagnetic Hall-like, tensor structure' without giving the explicit tensor form of the current; this should be stated with indices in the main text near the constitutive relations.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their careful reading of our manuscript and for the constructive comments. We appreciate the positive assessment of the potential significance of the Weyl anomaly-induced transport and the dual derivation approach. We address each major comment below and will incorporate clarifications in the revised version.

read point-by-point responses

Referee: [§3] §3 (hydrodynamic anomaly matching): The central claim that the trace-anomaly extension fixes the second-order coefficient without new undetermined parameters or consistency violations requires the explicit constitutive relation for the vector current and the precise matching condition (e.g., the relevant Ward identity or conservation equation) that determines the coefficient. Without this, the uniqueness cannot be verified from the text.

Authors: We agree that greater explicitness will aid verification. In the revised manuscript we will insert the explicit constitutive relation for the vector current, J^μ = (σ_E a^μ F_ν^λ u_λ + σ_B ε^μνρσ u_ν a_ρ B_σ) + O(∂^3), obtained by extending the hydrodynamic anomaly matching to the trace anomaly. The matching condition follows directly from the Ward identity ∇_μ T^μν = (anomaly term involving the Weyl tensor and electromagnetic invariants), which fixes the two second-order coefficients σ_E and σ_B without introducing new free parameters or violating conservation. This step-by-step derivation will be added to §3 to make the uniqueness manifest. revision: yes
Referee: [§4] §4 (Rindler boundary QFT): The boundary construction reproduces the same local coefficient. The manuscript must explicitly demonstrate that non-local horizon contributions (Unruh temperature, redshift factors, entanglement entropy) decouple in the local hydrodynamic limit of flat-space accelerated frames; otherwise the agreement with the anomaly-matching result does not establish that the coefficient is purely local and trace-anomaly fixed.

Authors: We thank the referee for highlighting this subtlety. In the revised §4 we will add an explicit decoupling argument: in the local hydrodynamic limit (wavelengths much shorter than the acceleration scale), the Unruh temperature is absorbed into the local fluid temperature T, redshift factors are removed by the choice of local inertial coordinates, and entanglement-entropy contributions appear only at non-local orders that vanish upon taking the flat-space limit while keeping the acceleration finite. With these terms shown to decouple, the boundary calculation reduces to a purely local, trace-anomaly-determined coefficient that matches the hydrodynamic result. revision: yes

Circularity Check

0 steps flagged

No circularity: derivation relies on independent standard methods

full rationale

The paper extends the established hydrodynamic anomaly-matching procedure to incorporate the trace anomaly and independently reproduces the result via boundary QFT treating the Rindler horizon as an effective boundary. Both steps are presented as applications of external, pre-existing techniques without self-definitional equations, fitted inputs renamed as predictions, or load-bearing self-citations that reduce the central coefficient to the paper's own inputs by construction. The abstract and description give no indication that the uniqueness or value of the transport coefficient is forced by prior author work or internal fitting; the result is therefore self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The central claim rests on the validity of extending hydrodynamic anomaly matching to the trace anomaly and on the equivalence of the Rindler-horizon boundary description to local accelerated-frame physics; no free parameters or new entities are mentioned.

axioms (2)

domain assumption Hydrodynamic anomaly matching extends consistently to the trace anomaly
Invoked as the primary derivation method in the abstract.
domain assumption Rindler horizon of an accelerated observer functions as an effective boundary in QFT
Used for the independent boundary-QFT reproduction.

pith-pipeline@v0.9.0 · 5468 in / 1321 out tokens · 37406 ms · 2026-05-08T05:40:29.071347+00:00 · methodology

discussion (0)

Reference graph

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