Chiral Separation Effect vs. Chiral Anomaly

TL;DR

This paper investigates the relationship between the Chiral Separation Effect and Chiral Anomaly, revealing that CSE is an IR effect sensitive to non-perturbative interactions, unlike the UV-fixed anomaly.

Contribution

It demonstrates that CSE is not an immutable consequence of the Chiral Anomaly and depends on IR properties and interactions, unlike the anomaly itself.

Findings

CSE is an IR effect, sensitive to non-perturbative interactions.

Chiral Anomaly is an UV phenomenon fixed by Lorentz symmetry.

CSE can be altered by interactions like fermion mass.

Abstract

We study relation between Chiral Separation Effect (CSE) and Chiral Anomaly, and argue that CSE does not inherit the immutability of Chiral Anomaly. For QED in the leading order in electric charge, with point-splitting regularization in real-time formalism, we demontrate, in regularization-dependent way though, that CSE is an infrared (IR) effect, while the Anomaly is an ultra-violet (UV) phenomena. Thus, CSE in general is sensitive to non-perturbative interactions that alter the theory IR properties, while the Anomaly is fixed by Lorentz symmetry. The simplest example of such an interaction is the Yukawa-like fermion mass.