Soliton fermionic number from the heat kernel expansion

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 η function that provides a more systematic version of the derivative expansion for spectral asymmetry and compute the fermion number in a multi flavor extension of the Goldstone–Wilczek model. We also propose an improved expansion of the heat kernel that allows the tackling of the convergence issues and permits an automated computation of the coefficients