(Non)-Renormalization of the Chiral Vortical Effect Coefficient

TL;DR

This paper investigates the conditions under which the chiral vortical effect coefficient remains unaffected by interactions, revealing cases of non-renormalization linked to topological quantization and cases where it is renormalized due to dynamical gauge fields.

Contribution

It provides a diagrammatic analysis of the temperature dependence of the CVE coefficient, connecting it to 3D Chern-Simons theory and clarifying when it is protected from renormalization.

Findings

Temperature-dependent CVE coefficient can be coupling independent in some cases.

Quantization in 3D Chern-Simons theory explains the non-renormalization in certain regimes.

Dynamical gauge fields lead to renormalization of the CVE coefficient, even at large N.

Abstract

We show using diagramtic arguments that in some (but not all) cases, the temperature dependent part of the chiral vortical effect coefficient is independent of the coupling constant. An interpretation of this result in terms of quantization in the effective 3 dimensional Chern-Simons theory is also given. In the language of 3D dimensionally reduced theory, the value of the chiral vortical coefficient is related to the formula $\sum_{n=1}^\infty n=-1/12$. We also show that in the presence of dynamical gauge fields, the CVE coefficient is not protected from renormalization, even in the large $N$ limit.