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Volume 363 - 37th International Symposium on Lattice Field Theory (LATTICE2019) - Main session
A physicist-friendly reformulation of the Atiyah-Patodi-Singer index and its mathematical justification
H. Fukaya,* M. Furuta, S. Matsuo, T. Onogi, S. Yamaguchi, M. Yamashita
*corresponding author
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Pre-published on: 2020 January 03
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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.
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