Speaker
Hidenori Fukaya
(Osaka Univ.)
Description
We employ $K$-theory to classify the Wilson Dirac operators to study gauge field topology on the lattice. 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.
Authors
Shoto Aoki
(RIKEN iTHEMS)
Hajime Fujita
Hidenori Fukaya
(Osaka Univ.)
Mikio Furuta
Shinichiroh Matsuo
Tetsuya Onogi
Satoshi Yamaguchi
(The University of Osaka)