# Chiral kinetic theory in curved spacetime

## TL;DR

This paper develops a covariant kinetic theory for chiral fermions in curved spacetime, enabling analysis of gravitational and non-inertial effects on chiral transport phenomena like the chiral vortical effect.

## Contribution

It derives a new covariant kinetic framework for chiral fermions in curved spacetime, incorporating gauge, Lorentz, and diffeomorphic invariance, and applies it to study the CVE in rotating systems.

## Key findings

- CVE is shown to be an intrinsic property of rotating chiral fluids.
- The framework clarifies the roles of Coriolis force and spin-vorticity coupling.
- Chiral vortical effect is independent of the observer's frame.

## Abstract

Many-body systems with chiral fermions exhibit anomalous transport phenomena originated from quantum anomalies. Based on quantum field theory, we derive the kinetic theory for chiral fermions interacting with an external electromagnetic field and a background curved geometry. The resultant framework respects the covariance under the U(1) gauge, local Lorentz, and diffeomorphic transformations. It is particularly useful to study the gravitational or non-inertial effects for chiral systems. As the first application, we study the chiral dynamics in a rotating coordinate and clarify the roles of the Coriolis force and spin-vorticity coupling in generating the chiral vortical effect (CVE). We also show that the CVE is an intrinsic phenomenon of a rotating chiral fluid, and thus independent of observer's frame.