Capturing the Atiyah-Patodi-Singer index from the lattice

arXiv (Cornell University) 2026 Preprint Open access

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Authors: Shoto Aoki, Hajime Fujita, Hidenori Fukaya, Mikio Furuta, Shinichiroh Matsuo, T. Onogi, Satoshi Yamaguchi
DOI: 10.48550/arxiv.2602.12576
Cited by: 0

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.

Fields of Study & Subjects

Quantum Chromodynamics and Particle Interactions Advanced Operator Algebra Research Spectral Theory in Mathematical Physics

Publication details

Journal / source
arXiv (Cornell University)
Publication date
13 February 2026
Language
EN
Document type
Preprint