The Chiral Magnetic Effect

TL;DR

The paper demonstrates that in a deconfined quark-gluon plasma with a chirality imbalance, an external magnetic field induces an electric current along its direction—the Chiral Magnetic Effect. Through four complementary derivations, the authors show the current magnitude J = (e^2 μ5 / 2π^2) B in the massless limit, linking the effect to the axial and electromagnetic anomalies. They explore how J depends on the chiral charge n5, magnetic-field strength, temperature, and baryon chemical potential, and discuss implications for heavy-ion collisions and potential experimental signals. The work also considers limitations due to fermion masses, chiral condensates, and potential applications like a chiral battery, highlighting CME as a probe of topological gauge configurations and CP-violation in QCD. Overall, the CME provides a robust, anomaly-driven mechanism for charge separation in strong magnetic fields, with broad implications for QCD, astrophysics, and condensed-matter analogues.

Abstract

Topological charge changing transitions can induce chirality in the quark-gluon plasma by the axial anomaly. We study the equilibrium response of the quark-gluon plasma in such a situation to an external magnetic field. To mimic the effect of the topological charge changing transitions we will introduce a chiral chemical potential. We will show that an electromagnetic current is generated along the magnetic field. This is the Chiral Magnetic Effect. We compute the magnitude of this current as a function of magnetic field, chirality, temperature, and baryon chemical potential.

Figures (6)

• Figure 1: Spectrum of massless Dirac fermions with right- and left-handed chirality in the presence of an chiral chemical potential $\mu_5$. The subscript $\pm$ denotes the eigenvalue of the spin in the $z$-direction. The chiral chemical potential induces a nonzero density of right-handed particles and left-handed anti-particles.
• Figure 2: Chiral Magnetic conductivity as a function of temperature and chemical potential. The dashed line is the high-temperature/chemical potential approximation.
• Figure 3: Current as a function of flux for $T=0$.
• Figure 4: Current at zero temperature in a homogeneous magnetic field as a function of magnetic field strength. The dashed line indicates the small field limit approximation.
• Figure 5: Chiral Magnetic conductivity as a function of the inverse magnetic field strength at zero temperature and chemical potential.