Chern-Simons term at finite density

TL;DR

This paper derives the Chern-Simons term coefficient at finite density, revealing how it depends on the chemical potential and mass, with implications for parity anomaly in odd dimensions.

Contribution

It provides a general derivation of the Chern-Simons term coefficient at arbitrary finite density, highlighting the critical role of the relation between chemical potential and mass.

Findings

Chern-Simons coefficient depends on the relation between μ^2 and m^2

The Chern-Simons term disappears when μ^2 > m^2

Parity anomaly is absent at finite density for massless fermions

Abstract

The Chern-Simons topological term coefficient is derived at arbitrary finite density. As it occures that $\mu^2 = m^2$ is the crucial point for Chern-Simons. So when $\mu^2 < m^2 \mu$--influence disappears and we get the usual Chern-Simons term. On the other hand when $\mu^2 > m^2$ the Chern-Simons term vanishes because of non-zero density of background fermions. In particular for massless case parity anomaly is absent at any finite density. This result holds in any odd dimension as in abelian so as in nonabelian cases.