2020/01/06 by Hidenori Fukaya, Mikio Furuta, Fukaya, Hidenori +9
Materials Science · Physics and Astronomy · #Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #Graphene research and applications #High Energy Physics - Lattice (hep-lat) #High Energy Physics - Theory (hep-th) #Quantum and electron transport phenomena #Strongly Correlated Electrons (cond-mat.str-el) #Topological Materials and Phenomena
paper · pdf · doi:10.48550/arxiv.2001.01428
openalex publication_date 2020/01/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The Atiyah-Patodi-Singer index theorem describes the bulk-edge correspondence of symmetry protected topological insulators. The mathematical setup for this theorem is, however, not directly related to the physical fermion system, as it imposes on the fermion fields a non-local and unnatural boundary condition known as the "APS boundary condition" by hand. In 2017, we showed that the same integer as the APS index can be obtained from the η invariant of the domain-wall Dirac operator. Recently we gave a mathematical proof that the equivalence is not a coincidence but generally true. In this contribution to the proceedings of LATTICE 2019, we try to explain the whole story in a physicist-friendly way.