Finite Temperature Induced Fermion Number for Quarks in a Chiral Field

TL;DR

This paper calculates how finite temperature affects the induced fermion number in a chiral background, revealing non-topological corrections and implications for nucleon models.

Contribution

It introduces a method to compute finite temperature corrections to fermion number in chiral fields, showing non-topological effects at nonzero temperature.

Findings

Finite temperature introduces non-topological corrections to fermion number.

Standard fractional fermion number cancellation does not occur at nonzero temperature.

Higher order derivative terms are crucial for understanding temperature effects.

Abstract

We compute the finite temperature correction to the induced fermion number for fermions coupled to a static SU(2) chiral background, using the derivative expansion technique. At zero temperature the induced fermion number is topological, being the winding number of the chiral background. At finite temperature however, higher order terms in the derivative expansion give nontopological corrections to the winding number. We use this result to show that the standard cancellation of the fractional parts of the fermion number inside and outside the bag in an SU(2) x SU(2) hybrid chiral bag model of the nucleon does not occur at nonzero temperature.