Saved in:
| Main Authors: | , , , , , |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2407.17708 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866916770723397632 |
|---|---|
| author | Aoki, Shoto Fukaya, Hidenori Furuta, Mikio Matsuo, Shinichiroh Onogi, Tetsuya Yamaguchi, Satoshi |
| author_facet | Aoki, Shoto Fukaya, Hidenori Furuta, Mikio Matsuo, Shinichiroh Onogi, Tetsuya Yamaguchi, Satoshi |
| contents | We mathematically show an equality between the index of a Dirac operator on a flat continuum torus and the $η$ invariant of a lattice Dirac operator known as the Wilson Dirac operator with a negative mass when the lattice spacing is sufficiently small. Unlike the standard approach, our formulation using $K$-theory does not require modified chiral symmetry on the lattice. We prove that a one-parameter family of continuum massive Dirac operators and the corresponding Wilson Dirac operators belong to the same equivalence class of the $K^1$ group at a finite lattice spacing. Their indices, which are evaluated by the spectral flow or equivalently by the $η$ invariant at a finite mass, are proved to be equal. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_17708 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The index of lattice Dirac operators and $K$-theory Aoki, Shoto Fukaya, Hidenori Furuta, Mikio Matsuo, Shinichiroh Onogi, Tetsuya Yamaguchi, Satoshi K-Theory and Homology Strongly Correlated Electrons High Energy Physics - Lattice High Energy Physics - Theory Differential Geometry We mathematically show an equality between the index of a Dirac operator on a flat continuum torus and the $η$ invariant of a lattice Dirac operator known as the Wilson Dirac operator with a negative mass when the lattice spacing is sufficiently small. Unlike the standard approach, our formulation using $K$-theory does not require modified chiral symmetry on the lattice. We prove that a one-parameter family of continuum massive Dirac operators and the corresponding Wilson Dirac operators belong to the same equivalence class of the $K^1$ group at a finite lattice spacing. Their indices, which are evaluated by the spectral flow or equivalently by the $η$ invariant at a finite mass, are proved to be equal. |
| title | The index of lattice Dirac operators and $K$-theory |
| topic | K-Theory and Homology Strongly Correlated Electrons High Energy Physics - Lattice High Energy Physics - Theory Differential Geometry |
| url | https://arxiv.org/abs/2407.17708 |