Chiral And Parity Anomalies At Finite Temperature And Density

TL;DR

This paper investigates how chiral and parity anomalies behave at finite temperature and density, revealing critical conditions for the Chern-Simons term and its independence from density and temperature.

Contribution

It demonstrates the conditions under which the Chern-Simons term appears or vanishes at finite density and temperature, generalizing the connection to chiral anomaly across dimensions.

Findings

Chern-Simons term depends on the relation between chemical potential and mass.

Chiral anomaly remains unaffected by temperature and density.

Results are applicable to both abelian and nonabelian gauge theories.

Abstract

Two closely related topological phenomena are studied at finite density and temperature. These are chiral anomaly and Chern-Simons term. 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. It is occurs that the chiral anomaly doesn't depend on density and temperature. The connection between parity anomalous Chern-Simons and chiral anomaly is generalized on finite density. These results hold in any dimension as in abelian, so as in nonabelian cases.