Speaker
Hidenori Fukaya
(Osaka Univ.)
Description
We mathematically show an equality between the index of a Dirac operator on a flat continuum torus and the $\eta$ invariant of the Wilson Dirac operator with a negative mass when the lattice spacing is sufficiently small. Unlike the standard approach, our formulation using the $K$-theory does not require the Ginsparg-Wilson relation or the 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 $K^1$ group at a finite lattice spacing. Their indices, which are evaluated by the spectral flow or equivalently by the $\eta$ invariant at finite masses, are proved to be equal.
Authors
Dr
Shoto Aoki
(U. Tokyo, Komaba)
Hidenori Fukaya
(Osaka Univ.)
Prof.
Mikio Furuta
(U. Tokyo, Komaba)
Prof.
Shinichiroh Matsuo
(Nagoya U.)
Prof.
Tetsuya Onogi
(Osaka Univ.)
Prof.
Satoshi Yamaguchi
(Osaka Univ.)