Capturing the Atiyah-Patodi-Singer index from the lattice
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arXiv
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| Autores principales: | , , , , , , |
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866908950155231232 |
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| author | Aoki, Shoto Fujita, Hajime Fukaya, Hidenori Furuta, Mikio Matsuo, Shinichiroh Onogi, Tetsuya Yamaguchi, Satoshi |
| author_facet | Aoki, Shoto Fujita, Hajime Fukaya, Hidenori Furuta, Mikio Matsuo, Shinichiroh Onogi, Tetsuya Yamaguchi, Satoshi |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_12576 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Capturing the Atiyah-Patodi-Singer index from the lattice Aoki, Shoto Fujita, Hajime Fukaya, Hidenori Furuta, Mikio Matsuo, Shinichiroh Onogi, Tetsuya Yamaguchi, Satoshi Differential Geometry High Energy Physics - Lattice High Energy Physics - Theory Geometric Topology K-Theory and Homology 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. |
| title | Capturing the Atiyah-Patodi-Singer index from the lattice |
| topic | Differential Geometry High Energy Physics - Lattice High Energy Physics - Theory Geometric Topology K-Theory and Homology |
| url | https://arxiv.org/abs/2602.12576 |