Anomalous Correction to Dynamical Response of Relativistic Plasma in a Magnetic Field

We study collective excitations in a relativistic collisionless plasma composed of massless fermions subject to an external magnetic field. We include dynamical electromagnetism and fluctuations of the chiral charge, while maintaining a vanishing net chiral charge. Within the framework of chiral kinetic theory, we find that the chiral anomaly gives a correction to the dispersion relation of the transverse mode. In a strong magnetic field, we also show that the collective mode has a gap using the lowest Landau level approximation. We discuss the anomalous correction in the context of neutron star phenomenology.