Nontopological Finite Temperature Induced Fermion Number

TL;DR

This paper investigates how finite temperature affects the induced fermion number in chiral sigma models, revealing dependence on background shape at finite temperature and topological invariance for certain backgrounds.

Contribution

It demonstrates that finite temperature modifies the fermion number dependence on background shape and provides a resummed low-temperature expansion for physical interpretation.

Findings

Finite temperature induces shape dependence in fermion number.

Resummed low-temperature expansion clarifies virtual pairs and thermal particles effects.

Kink backgrounds retain topological fermion number at finite temperature.

Abstract

We show that while the zero temperature induced fermion number in a chiral sigma model background depends only on the asymptotic values of the chiral field, at finite temperature the induced fermion number depends also on the detailed shape of the chiral background. We resum the leading low temperature terms to all orders in the derivative expansion, producing a simple result that can be interpreted physically as the different effect of the chiral background on virtual pairs of the Dirac sea and on the real particles of the thermal plasma. By contrast, for a kink background, not of sigma model form, the finite temperature induced fermion number is temperature dependent but topological.