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arXiv · 2505.20180

Vortex Fractional Fermion Number through Heat Kernel methods and Edge States

Sylvain Fichet·Rodrigo Fresneda·Lucas de Souza·Dmitri Vassilevich
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Abstract

Computing the vacuum expectation of fermion number operator on a soliton background is often challenging. A recent proposal in arXiv:2305.13606 simplifies this task by considering the soliton in a bounded region and relating the $\eta$ 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 (ANO) vortex background. We show that the resulting $\eta$ 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 fractional charge.

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Sylvain Fichet, Rodrigo Fresneda, Lucas de Souza, Dmitri Vassilevich. 2025-05-26. Vortex Fractional Fermion Number through Heat Kernel methods and Edge States. https://doi.org/10.1103/bzrd-n1hj

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