Notes on Anomaly Induced Transport

Abstract

Chiral anomalies give rise to dissipationless transport phenomena such as the chiral magnetic and vortical effects. In these notes I review the theory from a quantum field theoretic, hydrodynamic and holographic perspective. A physical interpretation of the otherwise somewhat obscure concepts of consistent and covariant anomalies will be given. Vanishing of the CME in strict equilibrium will be connected to the boundary conditions in momentum space imposed by the regularization. The role of the gravitational anomaly will be explained. That it contributes to transport in an unexpectedly low order in the derivative expansion can be easiest understood via holography. Anomalous transport is supposed to play also a key role in understanding the electronics of advanced materials, the Dirac-and Weyl (semi)metals. Anomaly related phenomena such as negative magnetoresistivity, anomalous Hall effect, thermal anomalous Hall effect and Fermi arcs can be understood via anomalous transport. Finally I briefly review a holographic model of Weyl semimetal which allows to infer a new phenomenon related to the gravitational anomaly: the presence of odd viscosity.

Chiral magnetic plasmons in anomalous relativistic matter

“…Indeed, the first term in Eq. (20) with b 0 = −µ 5 /e is exactly what is necessary to cancel the CME current in the equilibrium state [49]. Furthermore, the second term in δj describes the anomalous Hall effect in Weyl materials [51][52][53],…”

“…Here we took into account that the CME should be absent in equilibrium, i.e., set µ 5 = −eb 0 [49]. Let us note that the topological corrections given by the last two terms in Eq.…”

“…[47] (for a clear exposition, see also Ref. [49]) that the correct physical currents, satisfying the local conservation of the electric charge, are the consistent currents. As we argued in Ref.…”

“…Thus, the correct formulation of the theory is the consistent chiral kinetic theory that utilizes the consistent definition of the electric current. The additional topological contribution to the current density reads [47][48][49][50]:…”

“…Such a correction restores the local conservation of the electric charge in the presence of generic electromagnetic and pseudoelectromagnetic fields. One of the consequences of the corrected definition is the vanishing CME in an equilibrated plasma [47,49]. Of course, testing the local charge (non-)conservation unambiguously may not be easy via an electron transport, which is in essence a global probe.…”