arxiv: 2605.04743 · v1 · submitted 2026-05-06 · ✦ hep-lat · hep-ph· hep-th

Recognition: unknown

Chiral Magnetic Effect and Negative Magnetoresistance across the phase diagram of finite-density SU(2) gauge theory

P. V. Buividovich , L. von Smekal , D. Smith

Authors on Pith no claims yet

Pith reviewed 2026-05-08 15:22 UTC · model grok-4.3

classification ✦ hep-lat hep-phhep-th

keywords chiral magnetic effectnegative magnetoresistanceSU(2) gauge theoryfinite densitylattice simulationsquark gluon plasma

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The pith

The direct chiral magnetic effect signal in SU(2) gauge theory stays close to the free massless quark value across wide ranges of temperature and density.

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

This paper examines how the chiral magnetic effect manifests in lattice simulations of SU(2) gauge theory with two flavors of quarks at finite temperature and chemical potential, using a weak external magnetic field. By computing the vector-axial density correlator, they access the CME response directly, finding it depends only weakly on temperature and density in the quark-gluon plasma and matches the universal free-quark value. In contrast, the negative magnetoresistance extracted from vector current correlators is strongly suppressed at high temperatures or densities and falls below lowest-Landau-level expectations for free quarks. These results indicate that the two signatures of the CME do not track each other closely under the simulated conditions, and that phase transitions do not produce noticeable enhancements.

Core claim

The vector-axial correlator yields a CME response that is nearly independent of temperature and quark chemical potential in the plasma phase and equals the free massless quark value, while being only mildly reduced in the hadronic regime at low temperature and high density. The negative magnetoresistance signal, however, decreases sharply when either temperature or density is raised, and its overall size is smaller than the lowest Landau level prediction. No statistically significant boost in CME strength appears near the crossover or second-order transition lines in the phase diagram.

What carries the argument

The correlator between the axial charge density and the vector current, which directly measures the CME current, together with the two-point function of vector currents that encodes the longitudinal electric conductivity and thereby the negative magnetoresistance.

If this is right

The CME should be present with roughly constant strength throughout the quark-gluon plasma region at moderate magnetic fields.
Negative magnetoresistance is not a reliable indicator of the CME when magnetic fields are weak compared to the pion mass squared.
The CME is not particularly enhanced by proximity to the phase transition.
In the hadronic phase at large density the CME remains observable though slightly reduced.

Where Pith is reading between the lines

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

If the pattern holds in full QCD, analytic models may overestimate negative magnetoresistance in heavy-ion collisions at small magnetic fields.
The observed decoupling suggests that additional mechanisms beyond the lowest Landau level contribute to conductivity at weak fields.
Simulations with stronger magnetic fields could restore agreement with free-quark NMR predictions.

Load-bearing premise

The assumption that finite-volume effects, discretization errors, and the chosen weak value of the magnetic field do not distort the qualitative dependence of the measured correlators on temperature and density.

What would settle it

A calculation on significantly larger lattices or at stronger magnetic fields showing the vector-axial correlator deviating substantially from the free-quark value would falsify the reported near-universality.

Figures

Figures reproduced from arXiv: 2605.04743 by D. Smith, L. von Smekal, P. V. Buividovich.

**Figure 1.** Figure 1: At higher temperatures it shifts towards larger values of µ, goes through the chiral crossover region, and continues to higher densities and temperatures while still being a second-order transition [18–20]. Because of diquark condensation, SU(2) gauge theory can only be reliably compared with real QCD at sufficiently small µ. At very large densities and low temperatures, SU(2) gauge theory may also exhib… view at source ↗

**Figure 2.** Figure 2: FIG. 2. Axial-vector correlators view at source ↗

**Figure 3.** Figure 3: FIG. 3. The ratio of the CME coefficient extracted from the axial-vector correlator ( view at source ↗

**Figure 4.** Figure 4: FIG. 4. Correlators of vector currents as functions of Euclidean time view at source ↗

**Figure 5.** Figure 5: FIG. 5. Subtracted correlators of vector currents as functions of Euclidean time view at source ↗

**Figure 6.** Figure 6: FIG. 6. Mid-point estimates ( view at source ↗

**Figure 7.** Figure 7: FIG. 7. NMR coefficient view at source ↗

**Figure 8.** Figure 8: FIG. 8. NMR coefficient view at source ↗

read the original abstract

We study the signatures of the Chiral Magnetic Effect (CME) in $SU(2)$ gauge theory with $N_f = 2$ flavours of dynamical fermions at finite temperature $T$, quark chemical potential $\mu$ and a weak external magnetic field $e B$. We consider both the correlator of the axial density and the vector current, which gives direct access to the out-of-equilibrium CME, and the correlator of two vector currents, which probes the CME indirectly via the enhancement of the longitudinal electric conductivity (Negative Magnetoresistance, NMR). We find that the CME response extracted from the vector-axial correlator exhibits a rather weak dependence on temperature and density in the quark-gluon plasma regime, and is very close to the universal value for free massless quarks. The CME is mildly suppressed at low temperatures and large densities in the hadronic phase. In contrast, the NMR behaves in a qualitatively different way across the phase diagram, and is strongly suppressed at either large densities or temperatures. The magnitude of the NMR response appears to be considerably smaller than the prediction based on the lowest Landau level calculation for free quarks. Our findings suggest that for relatively small magnetic field strengths $e B \lesssim m_{\pi}^2$ the relation between the CME and NMR might not be as direct as expected. We also do not find statistically significant indications for an enhancement of the CME strength in the vicinity of the crossover or second-order phase transition lines in the $(\mu, T)$ phase diagram.

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 SU(2) lattice scan shows CME near the free value but NMR strongly suppressed, yet the suppression is the expected outcome for weak fields rather than evidence of decoupling.

read the letter

The paper runs dynamical-fermion SU(2) simulations with two flavors and maps both the direct CME signal from the axial-vector correlator and the indirect NMR signal from vector-vector correlators over the full (mu, T) plane at weak magnetic field. The CME response stays close to the universal free massless quark value through most of the plasma region and drops only mildly in the hadronic phase at high density. The NMR response falls sharply at high T or mu and sits well below the lowest-Landau-level free-quark estimate, with no statistically significant boost near the crossover or transition lines.

Referee Report

1 major / 2 minor

Summary. The paper presents lattice simulations of SU(2) gauge theory with two dynamical fermion flavors at finite temperature, chemical potential, and weak magnetic field. It extracts the Chiral Magnetic Effect (CME) from the vector-axial current correlator and Negative Magnetoresistance (NMR) from the vector-vector correlator. The results indicate that the CME response is close to the free massless quark value with weak dependence on T and μ in the QGP phase, mildly suppressed in the hadronic phase, while the NMR is strongly suppressed at high T or μ and its magnitude is considerably smaller than the lowest Landau level (LLL) free quark prediction, suggesting that the direct relation between CME and NMR may not hold for small magnetic fields eB ≲ m_π². No significant enhancement is found near phase transitions.

Significance. If the findings hold after addressing the benchmark issue, this work would be significant for providing non-perturbative lattice results on CME and NMR across the phase diagram in a controlled SU(2) theory with dynamical fermions at finite density. The numerical exploration of both direct (vector-axial) and indirect (vector-vector) signatures is a strength, as is the scan over the (μ, T) plane.

major comments (1)

[Abstract and NMR results section] Abstract and results/discussion of NMR: The claim that 'the magnitude of the NMR response appears to be considerably smaller than the prediction based on the lowest Landau level calculation for free quarks' and the inference that 'the relation between the CME and NMR might not be as direct as expected' for eB ≲ m_π² rests on an inappropriate free-theory benchmark. The LLL formula applies only in the strong-field regime (eB ≫ T², μ²) with only the lowest Landau level occupied; for the weak fields explicitly used here the correct free-fermion longitudinal conductivity enhancement requires the full sum over Landau levels (or weak-B expansion), which yields a much smaller effect that vanishes as B→0. The observed suppression is therefore the expected outcome of the regime mismatch rather than evidence for decoupling or interaction effects. This is load-bearing for the central interpretation.

minor comments (2)

[Abstract and methods] The manuscript provides no quantitative error bars, lattice volumes, number of configurations, or continuum-extrapolation details, making it difficult to assess the statistical significance of the reported trends and the comparison to free-quark limits.
[Methods and results] Clarify the precise definitions of the extracted CME and NMR responses (including any normalizations or fitting procedures) from the two correlators, and state the exact value of the weak magnetic field strength used in lattice units.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the careful and constructive review of our manuscript. We address the single major comment below, agreeing that the benchmark choice requires revision to accurately reflect the weak-field regime of our simulations.

read point-by-point responses

Referee: [Abstract and NMR results section] Abstract and results/discussion of NMR: The claim that 'the magnitude of the NMR response appears to be considerably smaller than the prediction based on the lowest Landau level calculation for free quarks' and the inference that 'the relation between the CME and NMR might not be as direct as expected' for eB ≲ m_π² rests on an inappropriate free-theory benchmark. The LLL formula applies only in the strong-field regime (eB ≫ T², μ²) with only the lowest Landau level occupied; for the weak fields explicitly used here the correct free-fermion longitudinal conductivity enhancement requires the full sum over Landau levels (or weak-B expansion), which yields a much smaller effect that vanishes as B→0. The observed suppression is therefore the expected outcome of the regime mismatch rather than evidence for decoupling or interaction effects. This is load-bear

Authors: We agree with the referee that the lowest Landau level (LLL) approximation for the free-fermion longitudinal conductivity applies strictly in the strong-field regime (eB ≫ T², μ²). Our simulations use weak magnetic fields satisfying eB ≲ m_π², where the appropriate free-theory benchmark is the full sum over Landau levels or the weak-B expansion, which produces a much smaller conductivity enhancement that vanishes as B → 0. The comparison to the LLL result in the abstract and discussion was intended as a common reference point from the CME literature, but we acknowledge that it leads to an inappropriate interpretation of the observed suppression. We will revise the abstract and the NMR results/discussion sections to remove the LLL comparison and the inference that the CME-NMR relation might not be direct. The revised text will instead note that the small NMR magnitude is consistent with weak-field free-fermion expectations while highlighting the contrasting weak T/μ dependence of the direct vector-axial CME correlator (which remains close to the free massless value). This change preserves the main numerical findings but corrects the central interpretation. revision: yes

Circularity Check

0 steps flagged

No significant circularity: lattice measurements compared to independent analytic benchmarks

full rationale

The paper reports direct lattice measurements of vector-axial and vector-vector correlators in SU(2) gauge theory with dynamical fermions. The CME response is extracted from the former and compared to the known universal value for free massless quarks; the NMR response from the latter is compared to the LLL free-quark formula. Neither comparison is obtained by fitting parameters to the target data, nor does any central claim reduce to a self-citation, self-definition, or ansatz smuggled from prior work by the same authors. The methodology follows standard lattice QCD practice and remains self-contained against external analytic results.

Axiom & Free-Parameter Ledger

1 free parameters · 2 axioms · 0 invented entities

The work rests on standard lattice gauge theory formalism and free-quark analytic results for comparison; no new entities are introduced and the only free parameters are the usual lattice spacing, bare mass, and simulation points in the (mu, T) plane.

free parameters (1)

lattice spacing and bare parameters
Chosen to reach physical scales and scan the phase diagram; values not specified in abstract.

axioms (2)

standard math Standard SU(2) lattice gauge action with Nf=2 dynamical fermions.
Invoked throughout as the simulation framework.
domain assumption Weak-field limit eB ≲ m_π² for interpreting correlators.
Stated explicitly when discussing relation to physical phenomena.

pith-pipeline@v0.9.0 · 5589 in / 1506 out tokens · 60243 ms · 2026-05-08T15:22:17.146354+00:00 · methodology

discussion (0)

Reference graph

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