Generalization of lattice Dirac operator index
Abstract
We provide a comprehensive lattice formulation of various types of the Dirac operator indices, employing -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.
Keywords
Cite
@article{arxiv.2602.22858,
title = {Generalization of lattice Dirac operator index},
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:2602.22858},
year = {2026}
}
Comments
10 pages, 3 figures, Talk presented at the 42nd International Symposium on Lattice Field Theory (LATTICE2025), 2-8 November 2025, Tata Institute of Fundamental Research, Mumbai, India