Fixed Charge Ensembles and Parity Breaking Terms

TL;DR

This paper explores how induced parity-breaking terms influence the free energy in fixed-charge ensembles for fermions in magnetic fields, highlighting the role of Chern-Simons terms in the thermodynamic properties.

Contribution

It demonstrates the impact of induced Chern-Simons terms on free energy dependence in fixed-charge ensembles with magnetic fields, extending previous results to finite temperature.

Findings

Free energy depends on magnetic flux and fixed charge relation.

Induced Chern-Simons term significantly affects thermodynamic behavior.

Results applicable to both Abelian and non-Abelian gauge fields.

Abstract

Recently derived results for the exact induced parity-breaking term in 2+1 dimensions at finite temperature are shown to be relevant to the determination of the free energy for fixed-charge ensembles. The partition functions for fixed total charge corresponding to massive fermions in the presence of Abelian and non-Abelian magnetic fields are discussed. We show that the presence of the induced Chern-Simons term manifests itself in that the free energy depends strongly on the relation between the external magnetic flux and the value of the fixed charge.