Capturing the Atiyah-Patodi-Singer index from the lattice
Differential Geometry
2026-04-13 v2 High Energy Physics - Lattice
High Energy Physics - Theory
Geometric Topology
K-Theory and Homology
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.
Keywords
Cite
@article{arxiv.2602.12576,
title = {Capturing the Atiyah-Patodi-Singer index from the lattice},
author = {Shoto Aoki and Hajime Fujita and Hidenori Fukaya and Mikio Furuta and Shinichiroh Matsuo and Tetsuya Onogi and Satoshi Yamaguchi},
journal= {arXiv preprint arXiv:2602.12576},
year = {2026}
}
Comments
43pages, 4 figures, generalization to cases without product metric near the boundary added