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Vortex fractional fermion number through heat kernel methods and edge states

Sylvain Fichet*

Rodrigo Fresneda†, Lucas de Souza‡, and Dmitri Vassilevich§

  • *Contact author: sylvain.fichet@gmail.com
  • †Contact author: rodrigo.fresneda@ufabc.edu.br
  • ‡Contact author: souza.l@ufabc.edu.br
  • §Contact author: dvassil@gmail.com
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Phys. Rev. D 112, 056009 – Published 11 September, 2025

DOI: https://doi.org/10.1103/bzrd-n1hj

Abstract

Computing the vacuum expectation of a fermion number operator on a soliton background is often challenging. A recent proposal in [1] simplifies this task by considering the soliton in a bounded region and relating the η invariant, and thus the fermion number, to a specific heat kernel coefficient and to contributions from the edge states. We test this method in a system of charged fermions living on an Abrikosov-Nielsen-Olesen vortex background. We show that the resulting η invariant does not depend on boundary conditions (within a certain class), thereby supporting the validity of the method. Our analysis reveals a nontrivial feature for the fermionic spectrum in the vortex-induced Higgs phase. As a by-product, we also find that for a vortex living on a disk, the edge states carry a fractional charge.

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Phys. Rev. D 112, 056009– Published 11 September, 2025
  • Received 9 June 2025
  • Accepted 13 August 2025
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