Edge states and the $\eta$ invariant

Rodrigo Fresneda; Lucas de Souza; Dmitri Vassilevich

doi:10.1016/j.physletb.2023.138098

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arXiv · 2305.13606

Edge states and the $\eta$ invariant

Rodrigo Fresneda·Lucas de Souza·Dmitri Vassilevich

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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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Rodrigo Fresneda, Lucas de Souza, Dmitri Vassilevich. 2023-05-23. Edge states and the $\eta$ invariant. https://doi.org/10.1016/j.physletb.2023.138098

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