Topological Effects in Medium

TL;DR

This paper investigates topological phenomena like chiral anomaly and Chern--Simons term at finite density and temperature, revealing their dependence on physical parameters and establishing their interconnection across dimensions.

Contribution

It provides a comprehensive analysis of topological effects in various dimensions, highlighting conditions for the emergence and disappearance of Chern--Simons terms under different constraints.

Findings

Chiral anomaly is independent of density and temperature.

Chern--Simons term depends on chemical potential and mass, vanishing or appearing based on their relation.

The connection between parity anomalous Chern--Simons and chiral anomaly is established across dimensions.

Abstract

Two closely related topological phenomena are studied at finite density and temperature. These are chiral anomaly and Chern--Simons term. It occurs that the chiral anomaly doesn't depend on density and temperature. Chern-Simons term appearance in even dimensions is studied under two types of constraints: chiral and usual charges conservation. In odd dimensions, by using different methods it is shown that $\mu^2 = m^2$ is the crucial point for Chern--Simons at zero temperature. 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. The connection between parity anomalous Chern-Simons in odd dimension and chiral anomaly in even dimension is established at arbitrary density and temperature. These results hold in any dimension as in abelian, so as in nonabelian cases.