Radiative corrections to chiral separation effect in QED

TL;DR

This paper computes the leading radiative corrections to the axial current in the chiral separation effect within dense QED under a magnetic field, revealing nontrivial corrections contrary to previous assumptions.

Contribution

It demonstrates that the axial current in the chiral separation effect receives significant radiative corrections due to Fermi surface singularities, challenging the notion of a purely topological current.

Findings

Radiative corrections modify the axial current in dense QED.

Fermi surface singularities are responsible for these corrections.

The corrections are linear in the external magnetic field.

Abstract

We calculate the leading radiative corrections to the axial current in the chiral separation effect in dense QED in a magnetic field. Contrary to the conventional wisdom suggesting that the axial current should be exactly fixed by the chiral anomaly relation and is described by the topological contribution on the lowest Landau level in the free theory, we find in fact that the axial current receives nontrivial radiative corrections. The direct calculations performed to the linear order in the external magnetic field show that the nontrivial radiative corrections to the axial current are provided by the Fermi surface singularity in the fermion propagator at nonzero fermion density.