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arxiv: 2606.04841 · v1 · pith:VT5Z3TRVnew · submitted 2026-06-03 · ✦ hep-th · cond-mat.mes-hall· gr-qc

Chiral Transport in Metric-Affine Geometries

Miguel A. Vazquez-Mozo This is my paper

Pith reviewed 2026-06-28 05:09 UTC · model grok-4.3

classification ✦ hep-th cond-mat.mes-hallgr-qc
keywords anomalous transportchiral separationnonmetricitymetric-affine geometryaxial currentWeyl geometryfermionic fluidsanomaly polynomial
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The pith

Nonmetricity in Weyl geometries induces chiral separation effects in the axial current of fermionic fluids through vorticity and magnetic fields.

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

The paper establishes that anomalous transport in equilibrium fermionic fluids chirally coupled to background Weyl-type nonmetricity produces additional contributions to the axial-vector current. These appear as nonmetricity-mediated chiral separation effects driven by the fluid's vorticity and the Weyl magnetic field. The result follows from a formal descent analysis that encodes the anomaly polynomial's nonmetricity dependence in a Weyl-invariant four-form, followed by transgression to an equilibrium partition function. A sympathetic reader would care because the work extends standard anomalous transport to metric-affine settings where nonmetricity acts as a background field.

Core claim

In equilibrium fermionic fluids chirally coupled to background Weyl-type nonmetricity, the constitutive relation of the axial-vector current exhibits nonmetricity-mediated chiral separation effects driven by the fluid's vorticity and the Weyl magnetic field. This follows from evaluating the axial current from the equilibrium partition function obtained using transgression techniques after a descent analysis encodes the anomaly polynomial dependence on the nonmetricity tensor in a Weyl-invariant four-form. A second nonminimal coupling of fermionic matter to metric-affine geometries is also examined.

What carries the argument

Weyl-invariant four-form that encodes the anomaly polynomial's dependence on the nonmetricity tensor, used for descent analysis and transgression to the equilibrium partition function.

If this is right

  • The axial current constitutive relation acquires extra terms linear in vorticity and the Weyl magnetic field.
  • Chiral separation is mediated by nonmetricity in addition to standard electromagnetic or gravitational contributions.
  • The same mechanism applies to a second proposed nonminimal coupling of fermions to metric-affine geometries.
  • Equilibrium partition functions constructed via transgression capture these nonmetricity effects without explicit time dependence.

Where Pith is reading between the lines

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

  • The effects could appear in effective hydrodynamic descriptions of systems with geometric defects or strain-induced nonmetricity.
  • In dynamical metric-affine gravity the same couplings might source modified chiral vortical conductivities.
  • Analog condensed-matter realizations with engineered nonmetricity could test the predicted current terms.

Load-bearing premise

The anomaly polynomial's dependence on the nonmetricity tensor can be encoded in a Weyl-invariant four-form that permits a consistent transgression to an equilibrium partition function.

What would settle it

Direct computation of the axial current in a constant Weyl nonmetricity background with nonzero vorticity, checking whether the predicted separation terms appear in the constitutive relation.

read the original abstract

Anomalous transport in equilibrium fermionic fluids chirally coupled to background Weyl-type nonmetricity is studied. A formal descent analysis is carried out in which the dependence of the anomaly polynomial on the nonmetricity tensor is encoded in a Weyl invariant four-form. The constitutive relation of the axial-vector current is evaluated from the equilibrium partition function obtained using transgression techniques, showing the existence of nonmetricity-mediated chiral separation effects driven by the fluid's vorticity and the Weyl magnetic field. A second nonminimal coupling of fermionic matter to metric-affine geometries proposed in the literature is also discussed.

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.

Referee Report

1 major / 0 minor

Summary. The manuscript studies anomalous transport in equilibrium fermionic fluids chirally coupled to background Weyl-type nonmetricity in metric-affine geometries. A formal descent analysis encodes the anomaly polynomial's dependence on the nonmetricity tensor in a Weyl-invariant four-form, from which an equilibrium partition function is obtained via transgression techniques. The constitutive relation of the axial-vector current is then evaluated, revealing nonmetricity-mediated chiral separation effects driven by the fluid's vorticity and the Weyl magnetic field. A second nonminimal coupling of fermionic matter to metric-affine geometries is also discussed.

Significance. If the formal steps hold, the work extends anomalous hydrodynamics to include Weyl nonmetricity as a background field, yielding new constitutive relations for the axial current. This provides a systematic way to incorporate non-Riemannian effects into chiral transport, which may be relevant for gravitational anomalies or effective descriptions in modified gravity and condensed-matter analogs. The approach follows standard descent methods but applies them to a new geometric structure.

major comments (1)
  1. [Abstract] Abstract and method description paragraph: the central claim that the constitutive relation exhibits nonmetricity-mediated chiral separation effects rests on unshown intermediate steps; explicit expressions for the Weyl-invariant four-form, the transgression to the partition function, and the resulting current coefficients (including any dependence on vorticity and the Weyl magnetic field) are required to assess the derivation.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the detailed reading and the suggestion to strengthen the presentation of the derivation. We address the comment below and will revise the manuscript accordingly.

read point-by-point responses

  1. Referee: [Abstract] Abstract and method description paragraph: the central claim that the constitutive relation exhibits nonmetricity-mediated chiral separation effects rests on unshown intermediate steps; explicit expressions for the Weyl-invariant four-form, the transgression to the partition function, and the resulting current coefficients (including any dependence on vorticity and the Weyl magnetic field) are required to assess the derivation.

    Authors: We agree that the abstract and introductory method paragraph would benefit from greater explicitness to make the logical steps immediately verifiable. In the revised version we will augment the abstract and add a dedicated subsection (or expanded paragraph in Sec. II) that displays: (i) the explicit Weyl-invariant four-form obtained by descent from the anomaly polynomial after incorporating the nonmetricity dependence, (ii) the transgression integral that yields the equilibrium partition function, and (iii) the resulting constitutive coefficients for the axial current, with their explicit dependence on fluid vorticity and the Weyl magnetic field written out. These additions will not alter the formal results but will render the intermediate expressions transparent. revision: yes

Circularity Check

0 steps flagged

No significant circularity; derivation self-contained

full rationale

The paper performs a standard formal descent analysis starting from an anomaly polynomial whose nonmetricity dependence is encoded in a Weyl-invariant four-form, then applies transgression to obtain the equilibrium partition function and the axial current constitutive relation. No equations reduce by construction to fitted parameters, self-definitions, or load-bearing self-citations; the central result is obtained from the input anomaly polynomial and established transgression techniques without internal circularity.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The work rests on the standard anomaly polynomial for chiral fermions and the validity of transgression techniques for constructing the equilibrium partition function; no new free parameters or invented entities are introduced in the abstract.

axioms (2)
  • domain assumption The anomaly polynomial dependence on nonmetricity can be captured by a Weyl-invariant four-form.
    Invoked in the descent analysis step of the abstract.
  • domain assumption Transgression techniques yield a valid equilibrium partition function for the axial current.
    Used to obtain the constitutive relation.

pith-pipeline@v0.9.1-grok · 5619 in / 1239 out tokens · 22030 ms · 2026-06-28T05:09:37.918602+00:00 · methodology

discussion (0)

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