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Edge states and the $\eta$ invariant

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arxiv 2305.13606 v2 pith:TQOW6QDV submitted 2023-05-23 hep-th

Rodrigo Fresneda , Lucas de Souza , Dmitri Vassilevich This is my paper · ORCID
classification hep-th
keywords boundaryedgeinvariantstateschiralconditionsrelationbounded
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abstract

We propose a relation between the $\eta$ invariant on a manifold with boundary, the $\eta$ invariants of edge states, and the $\eta$ invariant in an infinite volume limit. With the example of planar fermions with bag and chiral bag boundary conditions we show that this relation holds whenever edge states are sufficiently well-localized near the boundary. As a by-product we show that the spectrum of edge modes for chiral bag boundary conditions is linear but bounded.

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  1. Vortex Fractional Fermion Number through Heat Kernel methods and Edge States

    hep-th 2025-05 conditional novelty 6.0 of 10

    For fermions on an Abrikosov-Nielsen-Olesen vortex, the vacuum fermion number equals [sgn(m+e sqrt(2) v)+sgn(m-e sqrt(2) v)] n/4, and disk edge states carry charge e/2.

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