Anomalous plasma: chiral magnetic effect and all that

Chiral anomalous effects in relativistic plasmas are reviewed. The essence of chiral separation and chiral magnetic effects is explained in simple terms. Qualitative differences between the two phenomena, both of which are triggered by background electromagnetic fields, are highlighted. It is shown how an interplay of the chiral separation and chiral magnetic effects could lead to a new collective plasma mode, called the chiral magnetic wave. It is argued that the chiral magnetic wave is overdamped in weakly interacting plasmas. Its fate in a strongly interacting quark-gluon plasma is less clear, especially in the presence of a superstrong magnetic field. The observational signatures of the chiral anomalous effects are discussed briefly.