Today 2025 May24 (Sat) 23:02 Etc/GMT-9

2025/06/12 13:30~2025/06/12 14:30

Seminar, 深谷英則 Hidenori Fukaya (Osaka University)

Title: The index of lattice Dirac operators and K-theoryAbstract:We show that the Wilson Dirac operator in lattice gauge theory can be identified as a mathematical object in K-theory and that its associated spectral flow is equal to the index. In comparison to the standard lattice Dirac operator index, our formulation does not require the Ginsparg-Wilson relation and has broader applicability to systems with boundaries and to the mod-two version of the indices in general dimensions. We numerically verify that the K and KO group formulas reproduce the known index theorems in continuum theory. We examine the Atiyah-Singer index on a flat two-dimensional torus and, for the first time, demonstrate that the Atiyah-Patodi-Singer index with nontrivial curved boundaries, as well as the mod-two versions, can be computed on a lattice.