Second order chiral kinetic theory under gravity and antiparallel charge-energy flow

TL;DR

This paper develops a second-order chiral kinetic theory incorporating gravity, revealing new charge and energy transport phenomena due to spin-curvature coupling, with potential implications for condensed matter and high-energy physics.

Contribution

It introduces higher-order quantum corrections to chiral kinetic theory that add degrees of freedom for the distribution function, enabling the derivation of novel fermionic transport effects induced by gravity.

Findings

Charge and energy currents are antiparallelly induced by inhomogeneous vorticity.

New transport phenomena arise from spin-curvature coupling in gravitational fields.

Applications suggested for Weyl/Dirac semimetals and heavy-ion collisions.

Abstract

We derive the chiral kinetic theory under the presence of a gravitational Riemann curvature. It is well-known that in the chiral kinetic theory there inevitably appears a redundant ambiguous vector corresponding to the choice of the Lorentz frame. We reveal that on top of this conventional frame choosing vector, higher-order quantum correction to the chiral kinetic theory brings an additional degrees of freedom to specify the distribution function. Based on this framework, we derive new types of fermionic transport, that is, the charge current and energy-momentum tensor induced by the gravitational Riemann curvature. Such novel phenomena arise not only under genuine gravity but also in a (pseudo-)relativistic fluid, for which inhomogeneous vorticity or temperature are effectively represented by spacetime metric tensor. It is especially found that the charge and energy currents are antiparallelly induced by an inhomogeneous fluid vorticity (more generally, by the Ricci tensor ${R_0}^i$), as a consequence of the spin-curvature coupling. We also briefly discuss possible applications to Weyl/Dirac semimetals and heavy-ion collision experiments.