Chiral Magnetic Effect: Anomaly-Induced Currents

• Chiral Magnetic Effect is the generation of a non-dissipative electric current along magnetic fields in mediums with chirality imbalance due to the axial anomaly.
• It is observed in heavy-ion collisions where topological gluon fluctuations and spectator-generated magnetic fields create measurable charge-dependent azimuthal correlations.
• Theoretical models using hydrodynamics, holography, and chiral kinetics underpin CME, while experimental efforts continue to disentangle its signal from flow-related backgrounds.

Searching arXiv for recent and foundational papers on the Chiral Magnetic Effect to ground the article with relevant citations. to=arxiv_search ／久久് json {"query":"all:\"Chiral Magnetic Effect\" heavy ion review anomalous hydrodynamics holography experimental review", "max_results": 10, "sort_by": "relevance", "sort_order": "descending"} The Chiral Magnetic Effect (CME) is the generation of an electric current along a magnetic field in a medium with a chirality imbalance, and is widely understood as a macroscopic manifestation of the chiral anomaly. In relativistic heavy-ion collisions, the effect is sought in a quark–gluon plasma in which topological gluon-field fluctuations can generate local axial charge while spectator protons create a strong magnetic field approximately perpendicular to the reaction plane. In hydrodynamic language, the CME is encoded as a non-dissipative transport contribution of the form $\mathbf{J}_Q=\sigma_5\mathbf{B}$ with $\sigma_5=C_A\mu_5$, where $\mu_5$ is the chiral chemical potential and $C_A$ is fixed by the anomaly (Jiang et al., 2016).

1. Definition and anomaly origin

The defining constitutive relation of the CME is the magnetic-field-induced vector current

$$\mathbf{J}_Q=\sigma_5\mathbf{B}, \qquad \sigma_5=C_A\mu_5,$$

which differs qualitatively from ordinary Ohmic response $\mathbf{J}_Q=\sigma_e\mathbf{E}$ because the CME current is non-dissipative. Here $\mu_5$ quantifies the imbalance between right-handed and left-handed fermions, while the anomaly coefficient is fixed by charge and color; for a fermion with electric charge $Q_f$ and color factor $N_c$, one convention gives

$C_A=\frac{N_cQ_f^2}{2\pi^2}.$

In the chiral-current formulation used in anomalous hydrodynamics, the current of chirality $\sigma_5=C_A\mu_5$0 and flavor $\sigma_5=C_A\mu_5$1 contains the term

$\sigma_5=C_A\mu_5$2

which reproduces the standard $\sigma_5=C_A\mu_5$3 structure after summing over chiralities (Jiang et al., 2016).

The microscopic origin of the effect is the axial anomaly. In the presence of electromagnetic fields, the axial current is not conserved: $\sigma_5=C_A\mu_5$4 In heavy-ion and QCD contexts, topologically non-trivial gluon configurations, including instantons and sphalerons, change chirality and generate local axial charge domains. These domains fluctuate in sign event by event, so the average parity-odd dipole vanishes, while variance-like observables remain nonzero (Aziz, 2020).

A closely related integrated statement is the conservation of total helicity,

$\sigma_5=C_A\mu_5$5

with magnetic helicity $\sigma_5=C_A\mu_5$6 and fermionic helicity $\sigma_5=C_A\mu_5$7. This expresses that chirality can be exchanged between the fermionic sector and electromagnetic topology, and underlies the interpretation of CME as anomaly-induced transport rather than conventional conduction (Hirono, 2017).

2. Hydrodynamic, holographic, and kinetic formulations

In anomalous hydrodynamics, the CME appears as a first-order transport term in the vector current. For a plasma with multiple anomalous $\sigma_5=C_A\mu_5$8 currents, the first-order constitutive relation is written as

$\sigma_5=C_A\mu_5$9

where $\mu_5$0 is the vorticity four-vector and $\mu_5$1 is the magnetic conductivity. In the phenomenologically relevant two-charge system with vector and axial currents, the chiral magnetic conductivity is

$\mu_5$2

so that the leading piece is the standard anomaly-determined $\mu_5$3 term, while the subleading correction depends on thermodynamics through $\mu_5$4 (Kirsch et al., 2013).

A holographic fluid-gravity construction reproduces these hydrodynamic expressions exactly at strong coupling. In that framework, the anomaly is encoded by a five-dimensional Chern–Simons term, and the holographically extracted conductivities agree with the Son–Surowka-type formulas for $\mu_5$5 and $\mu_5$6. This is commonly interpreted as support for the universality of the anomaly-fixed part of the CME conductivity across weakly and strongly coupled regimes (Kirsch et al., 2013).

The same formal structure extends into chiral kinetic theory, where Berry-curvature corrections generate anomalous velocities and reproduce CME-like transport in out-of-equilibrium settings. In plasma applications, the CME modifies Maxwell–MHD evolution equations through an extra term in the induction equation,

$\mu_5$7

thereby producing a chiral dynamo instability with growth rate

$\mu_5$8

This broader chiral MHD perspective is central in early-Universe and high-energy plasma studies, but it also clarifies the dynamical interplay between anomaly-induced currents and electromagnetic fields in heavy-ion contexts (Schober et al., 2018).

3. Heavy-ion realization and dynamical modeling

Heavy-ion collisions provide the three ingredients usually invoked for CME: a hot chirally symmetric quark–gluon plasma, topological gluon fluctuations that generate axial charge, and an intense early-time magnetic field of order $\mu_5$9. The magnetic field is generated mainly by spectator protons in non-central collisions and is approximately perpendicular to the reaction plane (Liao, 2016).

A quantitative implementation of these ideas is the Anomalous Viscous Fluid Dynamics (AVFD) framework. AVFD uses a realistic 2+1D second-order viscous hydrodynamic evolution for the bulk medium and evolves right-handed and left-handed quark currents of each flavor as perturbations on top of that background. For each chirality $C_A$0 and flavor $C_A$1, AVFD solves

$C_A$2

together with

$C_A$3

and a second-order relaxation equation for the dissipative current $C_A$4. This setup includes both normal viscous transport and anomalous chiral transport and allows a realistic time-dependent modeling of CME in the expanding plasma (Jiang et al., 2016).

The magnetic field is modeled as

$C_A$5

with $C_A$6 taken from event-by-event electromagnetic simulations and $C_A$7 treated as an uncertain effective lifetime. Initial axial charge density is estimated from glasma topological fluctuations via a root-mean-square density scaling with the saturation scale $C_A$8, the flux-tube size, the initial time $C_A$9, the number of binary collisions, and the overlap area. Transport parameters such as $$\mathbf{J}_Q=\sigma_5\mathbf{B}, \qquad \sigma_5=C_A\mu_5,$$0 and $$\mathbf{J}_Q=\sigma_5\mathbf{B}, \qquad \sigma_5=C_A\mu_5,$$1 are used as canonical choices, while sensitivity studies indicate that the dominant uncertainties remain the initial axial charge and magnetic-field evolution rather than viscous transport coefficients (Jiang et al., 2016).

Event-by-event AVFD extends this framework to fluctuating initial conditions and incorporates known flow-driven backgrounds together with hadronic afterburner effects. In such simulations, the slope of $$\mathbf{J}_Q=\sigma_5\mathbf{B}, \qquad \sigma_5=C_A\mu_5,$$2 is essentially background-dominated, while the intercept grows quadratically with the initial axial charge, providing a practical separation between a flow-driven component and a CME-sensitive component (Shi et al., 2017).

4. Experimental observables and background structure

The canonical heavy-ion observable for CME is the three-particle-like correlator

$$\mathbf{J}_Q=\sigma_5\mathbf{B}, \qquad \sigma_5=C_A\mu_5,$$3

or, when the reaction plane is taken as the zero reference, $$\mathbf{J}_Q=\sigma_5\mathbf{B}, \qquad \sigma_5=C_A\mu_5,$$4. The single-particle charge distribution is commonly expanded as

$$\mathbf{J}_Q=\sigma_5\mathbf{B}, \qquad \sigma_5=C_A\mu_5,$$5

where $$\mathbf{J}_Q=\sigma_5\mathbf{B}, \qquad \sigma_5=C_A\mu_5,$$6 is the dipole coefficient. Because the sign of the initial axial charge fluctuates, $$\mathbf{J}_Q=\sigma_5\mathbf{B}, \qquad \sigma_5=C_A\mu_5,$$7 while $$\mathbf{J}_Q=\sigma_5\mathbf{B}, \qquad \sigma_5=C_A\mu_5,$$8 can be nonzero and is what $$\mathbf{J}_Q=\sigma_5\mathbf{B}, \qquad \sigma_5=C_A\mu_5,$$9-type observables probe indirectly (Jiang et al., 2016).

A standard decomposition writes

$\mathbf{J}_Q=\sigma_e\mathbf{E}$0

where the first term represents a flow-related background and $\mathbf{J}_Q=\sigma_e\mathbf{E}$1 is a flow-independent component. Under the assumption of a pure CME-induced dipole,

$\mathbf{J}_Q=\sigma_e\mathbf{E}$2

This makes $\mathbf{J}_Q=\sigma_e\mathbf{E}$3 the quantity most often treated as the experimentally extracted CME-sensitive component (Jiang et al., 2016).

The central experimental difficulty is that $\mathbf{J}_Q=\sigma_e\mathbf{E}$4 receives large background contributions from local charge conservation coupled with elliptic flow, resonance decays, cluster correlations, jets, and momentum conservation. Resonance and cluster backgrounds can be written schematically as

$\mathbf{J}_Q=\sigma_e\mathbf{E}$5

which already has the same harmonic structure as the sought CME signal. This is why small systems, invariant-mass methods, event-shape engineering, spectator-plane analyses, and isobar comparisons have all been pursued as background-mitigation strategies rather than relying on $\mathbf{J}_Q=\sigma_e\mathbf{E}$6 alone (Zhao, 2018).

More recently, higher-harmonic structure in differential $\mathbf{J}_Q=\sigma_e\mathbf{E}$7 has been proposed as a potentially cleaner handle. In that approach,

$\mathbf{J}_Q=\sigma_e\mathbf{E}$8

and the hexadecapole ratio

$\mathbf{J}_Q=\sigma_e\mathbf{E}$9

is argued to be sensitive to CME and insensitive to conventional backgrounds in model studies, because ordinary cluster-plus-flow backgrounds are dominantly quadrupolar while CME can inherit higher-harmonic structure from event-by-event magnetic-field fluctuations (Li et al., 25 May 2026).

5. Experimental status and controversies

Measurements with STAR, ALICE, CMS, and other programs have established robust charge-dependent azimuthal correlations, but not a conclusive CME observation. In ALICE Pb–Pb at $\mu_5$0 TeV and Xe–Xe at $\mu_5$1 TeV, the $\mu_5$2 correlator shows a significant charge dependence between opposite-sign and same-sign pairs, which is consistent with a CME-like signal. However, the background-sensitive $\mu_5$3 correlator in Xe–Xe also shows a significant charge dependence, preventing a clear interpretation of $\mu_5$4 and motivating the conclusion that novel methods are necessary (Aziz, 2020).

A particularly sharp challenge to a large CME interpretation comes from system comparisons. In ALICE data, Pb–Pb and Xe–Xe exhibit quantitatively close $\mu_5$5 correlators despite the magnetic field in Pb–Pb being several times stronger than in Xe–Xe at comparable centralities. If the measured correlator were dominated by CME, a stronger scaling with magnetic field would be expected. This is widely interpreted as evidence that backgrounds dominate the measured $\mu_5$6 (Aziz, 2020).

Small-system control measurements support the same conclusion. In STAR p+Au and d+Au collisions, where the magnetic field is not expected to correlate with the participant plane strongly enough to yield a measurable CME with respect to the event plane, the scaled correlator remains comparable to that in Au+Au at similar multiplicity. This suggests that peripheral and mid-central Au+Au $\mu_5$7 is largely driven by background. The invariant-mass dependence of $\mu_5$8 further shows that resonance-dominated regions account for most of the inclusive signal, while after a high-mass cut the remaining signal is consistent with zero within uncertainties (Zhao, 2018).

Yet the experimental picture is not entirely null. A STAR analysis comparing charge separation relative to spectator and participant planes in Au+Au at $\mu_5$9 GeV finds that, after removing flow-related background, the extracted charge separation is consistent with zero in peripheral collisions, but some indication of finite CME signals is seen in mid-central collisions. The paper explicitly cautions that significant residual background effects may still be present, so this is not treated as definitive evidence (Collaboration et al., 2021).

A recent experimental review summarizes the field’s status succinctly: no conclusive experimental evidence on the CME has been established so far because of large background contributions to azimuthal correlation observables. Existing methods constrain any CME fraction in standard correlators to be subdominant, while the spectator-plane method currently provides one of the strongest positive indications that remains under active scrutiny (Li et al., 10 Nov 2025).

6. Broader contexts, limitations, and future directions

The CME is not specific to heavy-ion collisions. Signals consistent with CME have been reported in Dirac and Weyl semimetals, and theoretical work on bounded Weyl semimetal wires shows that, in an oscillating magnetic field, an adiabatic CME can persist in the $Q_f$0 limit, with boundary states significantly altering or even dominating the response. This broader condensed-matter context reinforces the universality of anomaly-induced transport while also illustrating that geometry, boundaries, and equilibrium versus non-equilibrium limits matter crucially for observable manifestations (Ivashko et al., 2017).

The effect also appears in astrophysical and plasma settings. In chiral MHD, the CME adds a term to the induction equation that can drive a dynamo instability and inverse cascade. In a different nonequilibrium setting, neutrino radiation in core-collapse supernovae has been shown to induce an effective CME-like current along magnetic fields even without a chiral chemical potential, through weak-interaction-driven nonequilibrium corrections to electron distributions (Yamamoto et al., 2022).

Within QCD itself, there are also conceptual challenges to a large CME in the quark–gluon plasma. One argument invokes the approximate emergence of chiral spin symmetry above $Q_f$1: because $Q_f$2 mixes right-handed and left-handed quark components, an exact chiral spin symmetry would forbid chirality imbalance and thus require $Q_f$3. Since lattice studies indicate approximate chiral spin symmetry with symmetry breaking at the level of a few percent, this has been proposed as a symmetry-based explanation for a very small or vanishing CME signal in heavy-ion collisions (Glozman, 2020).

Future directions in heavy-ion CME searches are correspondingly twofold. On the theory side, better constraints are needed on magnetic-field lifetime, initial axial charge generation, transport coefficients, and pre-hydrodynamic anomalous transport, with AVFD and related anomalous hydrodynamic tools continuing to serve as signal simulators and benchmarking frameworks (Shi et al., 2017). On the experimental side, progress is centered on observables less degenerate with elliptic-flow backgrounds: spectator-versus-participant-plane comparisons, event-shape engineering, invariant-mass differential analyses, multi-plane correlators, and higher-harmonic observables such as the hexadecapole component of $Q_f$4 (Li et al., 25 May 2026).

A plausible implication is that the CME question in heavy-ion collisions has shifted from the existence of charge-dependent correlations—which is well established—to whether any statistically and systematically controlled component of those correlations can be isolated as anomaly-driven rather than flow-driven. On present evidence, the CME remains theoretically robust, experimentally elusive, and methodologically central to the study of anomalous transport in QCD matter (Li et al., 10 Nov 2025).