Generalization of lattice Dirac operator index
arXiv:2602.22858
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.
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