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arXiv · 2602.12576

Capturing the Atiyah-Patodi-Singer index from the lattice

Shoto Aoki·Hajime Fujita·Hidenori Fukaya·Mikio Furuta·Shinichiroh Matsuo·Tetsuya Onogi·Satoshi Yamaguchi
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Abstract

We construct a formulation of the Atiyah-Patodi-Singer index of Dirac operators in lattice gauge theory for domains with compact boundaries in a flat torus. The key idea is to exploit its equality to the spectral flow of the domain-wall fermion Dirac operators, which we generalize in this work to cases without product structure near the boundary. We prove that, for sufficiently small lattice spacings, this formulation correctly captures the continuum Atiyah-Patodi-Singer index.

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Shoto Aoki, Hajime Fujita, Hidenori Fukaya, Mikio Furuta, Shinichiroh Matsuo, Tetsuya Onogi, Satoshi Yamaguchi. 2026-04-10. Capturing the Atiyah-Patodi-Singer index from the lattice. https://arxiv.org/abs/2602.12576

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