Mixed Anomalies: Chiral Vortical Effect and the Sommerfeld Expansion

TL;DR

This paper explores the mathematical connection between Fermi distribution moments and anomalous conservation laws in chiral fermions, revealing how thermal effects like the chiral vortical effect originate from gravitational anomalies.

Contribution

It establishes a link between Sommerfeld expansion coefficients and chiral anomaly coefficients, providing a new method to derive thermal contributions to chiral transport phenomena.

Findings

Derived the chiral magneto-thermal energy current from mixed gauge-gravity anomaly.

Confirmed the T^2/12 thermal contribution to the chiral vortical effect arises from the gravitational Pontryagin term.

Linked Fermi distribution moments to anomalous conservation law coefficients.

Abstract

We discuss the connection between the integer moments of the Fermi distribution function that occur in the Sommerfeld expansion and the coefficients that occur in anomalous conservation laws for chiral fermions. As an illustration we extract the chiral magneto-thermal energy current from the mixed gauge-gravity anomaly in the 3+1 dimensional energy-momentum conservation law. We then use a similar method to confirm the conjecture that the $T^2/12$ thermal contribution to the chiral vortical effect (CVE) current arises from the gravitational Pontryagin term in the 3+1-dimensional chiral anomaly