# Index of the Wilson-Dirac operator revisited: a discrete version of Dirac operator on a finite lattice

- Date
- February 25 at 16:00 - 18:10, 2020

- Speaker
- Dr. Mikio Furuta (Professor, The University of Tokyo)

- Venue
- Seminar Room #160

- Language
- English

The Wilson-Dirac operator is a discrete version of Dirac operator defined on regular lattices. When the discrete version is a fine approximation of the Dirac operator on a Z/2-graded Clifford module on a torus, it is known that

(1) an integer-valued index is defined for the Wilson-Dirac operator, and

(2) the index is equal to the Atiyah-Singer index of the Dirac operator on the torus.

These have been well established up to around 2000. The strategy of all the previous works is to make use of the discrete version of the heat kernel for Neuberger's overlap Dirac operator. Therefore the strategy cannot be generalized to mod 2 index nor family version of index.

In this talk I would like to explain a new approach to the index of Wilson-Dirac operator which can be immediately generalized to these various cases.

Joint work with H. Fukaya, S. Matsuo, T. Onogi, S. Yamaguchi and M. Yamashita.