# Soliton Fermionic number from the heat kernel expansion

## TL;DR

This paper develops systematic heat kernel expansion methods to accurately compute the fractional fermion number of solitons, addressing convergence issues and enabling automated calculations in complex models.

## Contribution

It introduces a refined heat kernel expansion approach and a formula for the localized eta function, improving the calculation of fermion numbers in soliton models.

## Key findings

- Derived a systematic eta function formula for spectral asymmetry
- Proposed an improved heat kernel expansion addressing convergence
- Enabled automated computation of fermion numbers in multiflavour models

## Abstract

We consider different methods of calculating the (fractional) fermion number of solitons based on the heat kernel expansion. We derive a formula for the localized eta function a more systematic version of the derivative expansion for spectral assymmetry and that provides a more systematic version of the derivative expansion for spectral asymmetry and compute the fermion number in a multiflavour extension of the Goldstone-Wilczek model.We also propose an improved expansionof the heat kernelthat allows the tackling ofthe convergence issues and permits an automated computation of the coefficients