2021/12/01 by Hidenori Fukaya, Fukaya, Hidenori
Physics and Astronomy · #FOS: Physical sciences #High Energy Physics - Lattice (hep-lat) #High Energy Physics - Theory (hep-th) #Physics of Superconductivity and Magnetism #Quantum and electron transport phenomena #Topological Materials and Phenomena
paper · pdf · doi:10.48550/arxiv.2112.00261
openalex publication_date 2021/12/01 · openalex created_date 2022/05/05 · openalex updated_date 2026/07/28
The Atiyah-Singer index theorem on a closed manifold is well understood and appreciated in physics. On the other hand, the Atiyah-Patodi-Singer index, which is an extension to a manifold with boundary, is physicist-unfriendly, in that it is formulated with a nonlocal boundary condition. Recently we proved that the same index as APS is obtained from the domain-wall fermion Dirac operator. Our theorem indicates that the index can be expressed without any nonlocal conditions, in such a physicist-friendly way that application to the lattice gauge theory is straightforward. The domain-wall fermion provides a natural mathematical foundation for understanding the bulk-edge correspondence of the anomaly inflow.