Chiral and Gravitational Anomalies on Fermi Surfaces

TL;DR

This paper explores how Berry phase on Fermi surfaces leads to Chern-Simons terms that encode chiral and gravitational anomalies, revealing new effects like a temperature-gradient-induced contribution to the Chiral Vortical Effect.

Contribution

It demonstrates how the Wess-Zumino-Witten term and Chern-Simons action describe various anomalies and introduces a novel temperature-gradient effect in the Chiral Vortical Effect.

Findings

Chern-Simons terms encode chiral and gravitational anomalies.

Derived a new contribution to the Chiral Vortical Effect involving temperature gradients.

Discussed the universality of anomalous currents.

Abstract

A Fermi surface threaded by a Berry phase can be described by the Wess-Zumino-Witten (WZW) term. After gauging, it produces a five-dimensional Chern-Simons term in the action. We show how this Chern-Simons term captures the essence of the Abelian, non-Abelian, and mixed gravitational anomalies in describing both in- and off-equilibrium phenomena. In particular we derive a novel contribution to the Chiral Vortical Effect that arises when a temperature gradient is present. We also discuss the issue of universality of the anomalous currents.