Generalization of lattice Dirac operator index
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arXiv
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| Main Authors: | , , , , , , |
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| Format: | Preprint |
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2026
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| _version_ | 1866915818735927296 |
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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 provide a comprehensive lattice formulation of various types of the Dirac operator indices, employing $K$-theory to classify the Wilson Dirac operator via its spectral flow. In contrast to the index of the overlap Dirac operator defined through the Ginsparg-Wilson relation, which is restricted to flat tori in even dimensions, our formulation offers several key advantages: 1) It can be applied straightforwardly to the Atiyah-Patodi-Singer index for manifolds with boundary. 2) The boundary can be curved, allowing for the inclusion of gravitational background effects. 3) The mod-2 index in both even and odd dimensions can be defined as a natural extension of the same formulation. In this talk, we present the mathematical proof and provide numerical evidence supporting the formulation. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2602_22858 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Generalization of lattice Dirac operator index Aoki, Shoto Fujita, Hajime Fukaya, Hidenori Furuta, Mikio Matsuo, Shinichiroh Onogi, Tetsuya Yamaguchi, Satoshi High Energy Physics - Lattice High Energy Physics - Theory Differential Geometry We provide a comprehensive lattice formulation of various types of the Dirac operator indices, employing $K$-theory to classify the Wilson Dirac operator via its spectral flow. In contrast to the index of the overlap Dirac operator defined through the Ginsparg-Wilson relation, which is restricted to flat tori in even dimensions, our formulation offers several key advantages: 1) It can be applied straightforwardly to the Atiyah-Patodi-Singer index for manifolds with boundary. 2) The boundary can be curved, allowing for the inclusion of gravitational background effects. 3) The mod-2 index in both even and odd dimensions can be defined as a natural extension of the same formulation. In this talk, we present the mathematical proof and provide numerical evidence supporting the formulation. |
| title | Generalization of lattice Dirac operator index |
| topic | High Energy Physics - Lattice High Energy Physics - Theory Differential Geometry |
| url | https://arxiv.org/abs/2602.22858 |