2024/07/25 by Aoki, Shoto, Fukaya, Hidenori, Furuta, Mikio +3 · 1 citation
#Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #High Energy Physics - Lattice (hep-lat) #High Energy Physics - Theory (hep-th) #K-Theory and Homology (math.KT) #Strongly Correlated Electrons (cond-mat.str-el)
paper · doi:10.48550/arxiv.2407.17708
We mathematically show an equality between the index of a Dirac operator on a flat continuum torus and the η invariant of a lattice Dirac operator known as the Wilson Dirac operator with a negative mass when the lattice spacing is sufficiently small. Unlike the standard approach, our formulation using K-theory does not require modified chiral symmetry on the lattice. We prove that a one-parameter family of continuum massive Dirac operators and the corresponding Wilson Dirac operators belong to the same equivalence class of the K1 group at a finite lattice spacing. Their indices, which are evaluated by the spectral flow or equivalently by the η invariant at a finite mass, are proved to be equal.