Generalization of lattice Dirac operator index

by Hidenori Fukaya (Osaka Univ.)

Tuesday May 26, 2026, 10:00 AM → 11:30 AM Europe/Zurich

4/2-037 - TH meeting room (CERN)

We propose a comprehensive lattice formulation of various types of the
Dirac operator indices, employing K-theory to classify the Wilson
Dirac operator by 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 advantages: 1) The chiral symmetry is not essential at
all. 2) It can be applied straightforwardly to the
Atiyah-Patodi-Singer index for manifolds with boundary. 3) The
boundary can be curved, allowing for the inclusion of gravitational
background effects. 4) 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.
This talk is based on arXiv:2503.23921  and  2602.12576.