Chiral kinetic theory and anomalous hydrodynamics in even spacetime dimensions

Abstract

We study the hydrodynamics of a gas of noninteracting Weyl fermions coupled to the electromagnetic field in (2N + 1) + 1 spacetime dimensions using the chiral kinetic theory, which encodes the gauge anomaly in the Chern character of the nonabelian Berry connection over the Fermi surface.We derive the anomalous contributions to the relativistic hydrodynamic currents in equilibrium and at a finite temperature, which agree with and provides an approach complementary to the results derived previously using thermodynamic constraints.

Mixed Anomalies: Chiral Vortical Effect and the Sommerfeld Expansion

“…This impression was made concrete by Loganayagam and Surówka [4] who observed that a generating function for the integer moments of the Fermi function bears a close resemblance to the the product of the A-roof genus and the total Chern character that occurs in the general-dimension Dirac index theorem -and which, via the Bardeen-Zumino descent equations [5], is the ultimate source of the anomalies. Their observation lead them to a "replacement rule" that allowed them to compute anomaly-induced contributions to transport and fluid dynamics in N space-time dimensions directly from the anomaly polynomial in N + 2 dimensions [4,[6][7][8][9][10][11][12].…”