# The chiral anomaly, Berry's phase and chiral kinetic theory, from world-lines in quantum field theory

## TL;DR

This paper develops a new chiral kinetic theory framework using world-line formalism to compute the Chiral Magnetic Effect in heavy-ion collisions, connecting quantum anomalies, Berry's phase, and topological effects.

## Contribution

It introduces a covariant relativistic chiral kinetic theory derived from a supersymmetric world-line approach, incorporating topological fluctuations and anomaly effects.

## Key findings

- Expresses fermion determinant as a world-line action with Berry's phase
- Derives anomalous axial current from fermion determinant phase
- Provides a framework linking quantum anomalies with classical simulations

## Abstract

We outline a novel chiral kinetic theory framework for systematic computations of the Chiral Magnetic Effect (CME) in ultrarelativistic heavy-ion collisions. The real part of the fermion determinant in the QCD effective action is expressed as a supersymmetric world-line action of spinning, colored, Grassmanian point particles in background gauge fields, with equations of motion that are covariant generalizations of the Bargmann-Michel-Telegdi and Wong equations. Berry's phase is obtained in a consistent non-relativistic adiabatic limit. The chiral anomaly, in contrast, arises from the phase of the fermion determinant; its topological properties are therefore distinct from those of the Berry phase. We show that the imaginary contribution to the fermion determinant too can be expressed as a point particle world-line path integral and derive the corresponding anomalous axial vector current. Our results can be used to derive a covariant relativistic chiral kinetic theory including the effects of topological fluctuations that has overlap with classical-statistical simulations of the CME at early times and anomalous hydrodynamics at late times.