PoS - Proceedings of Science
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 and M. Yamashita
Full text: pdf
Pre-published on: January 03, 2020
Published on: August 27, 2020
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.
DOI: https://doi.org/10.22323/1.363.0061
How to cite

Metadata are provided both in "article" format (very similar to INSPIRE) as this helps creating very compact bibliographies which can be beneficial to authors and readers, and in "proceeding" format which is more detailed and complete.

Open Access
Creative Commons LicenseCopyright owned by the author(s) under the term of the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.