Chiral Magnetic Wave
Dmitri E. Kharzeev, Ho-Ung Yee
TL;DR
This work demonstrates that triangle anomalies in magnetized relativistic plasmas generate a new gapless collective mode, the Chiral Magnetic Wave (CMW), coupling electric and chiral charge density waves and propagating along the magnetic field. It derives and cross-validates the CMW across three frameworks: relativistic magnetohydrodynamics, strong-field dimensional reduction to a 1+1D Sine-Gordon description, and holographic QCD via the Sakai–Sugimoto model, revealing a nonperturbative, field-dependent wave velocity that approaches the speed of light at large $eB$. By incorporating dynamical electromagnetism, the study shows how CMW mixes with plasmons, altering plasmon dispersions and yielding Schwinger-type photon masses in strong fields. The results have potential implications for heavy-ion collision phenomenology, including reaction-plane dependent charge fluctuations, and establish a robust, multi-method confirmation of the CMW across weak and strong coupling regimes.
Abstract
We consider a relativistic plasma containing charged chiral fermions in an external magnetic field, e.g a chirally symmetric quark-gluon plasma created in relativistic heavy ion collisions. We show that triangle anomalies imply the existence of a new type of collective gapless excitation in this system that stems from the coupling between the density waves of the electric and chiral charges; we call it "the Chiral Magnetic Wave" (CMW). The CMW exists even in a neutral plasma, i.e. in the absence of the axial and vector chemical potentials. We demonstrate the existence of CMW and study its properties using three different approaches: i) relativistic magnetohydrodynamics; ii) dimensional reduction to $(1+1)$ Sine-Gordon model, appropriate in a strong magnetic field; and iii) holographic QCD (Sakai-Sugimoto model), appropriate at strong coupling. We also briefly discuss the phenomenological implications of the CMW for heavy ion collisions.