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arXiv 2001.014282020-01-06hep-latcond-mat.str-elhep-thmath.DG

A physicist-friendly reformulation of the Atiyah-Patodi-Singer index and its mathematical justification

Hidenori Fukaya, Mikio Furuta, Shinichiroh Matsuo, Tetsuya Onogi, Satoshi Yamaguchi, Mayuko Yamashita

备注：: 7 pages, talk presented at Lattice 2019

英文摘要：

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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