Conformal anomaly and helicity effects in kinetic theory via scale-dependent coupling

TL;DR

This paper extends kinetic theory for massless fermions by incorporating the conformal anomaly through a scale-dependent coupling, revealing effects on axial current and helicity flow in a collisionless regime.

Contribution

It introduces a novel method to include the conformal anomaly in kinetic theory using a momentum-dependent coupling, linking anomalies to observable helicity effects.

Findings

Conformal anomaly induces a hedgehog-like structure in momentum space.

Axial current is generated by the interplay of axial and conformal anomalies.

Conductivity depends on the running of the electric coupling from Dirac cone tip to Fermi surface.

Abstract

We modify a kinetic theory of massless fermions to incorporate the effects of the conformal anomaly. Working in a collisionless regime, we emulate the conformal anomaly via a momentum-dependent electric coupling. In this prescription, the conformal anomaly leads to a hedgehog-like structure in the momentum space similar to the Berry phase associated with the axial anomaly. The interplay between the axial and conformal anomalies generates the axial current, proportional to the helicity flow of the electromagnetic background. The corresponding conductivity is determined by the running of the electric coupling between the tip of the Dirac cone and the Fermi surface.