2025/03/31 by Aoki, Shoto, Fukaya, Hidenori, Furuta, Mikio +3 · 1 citation
#FOS: Mathematics #FOS: Physical sciences #High Energy Physics - Lattice (hep-lat) #High Energy Physics - Theory (hep-th) #K-Theory and Homology (math.KT)
paper · doi:10.48550/arxiv.2503.23921
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.