| Issue |
EPJ Web Conf.
Volume 175, 2018
35th International Symposium on Lattice Field Theory (Lattice 2017)
|
|
|---|---|---|
| Article Number | 11009 | |
| Number of page(s) | 8 | |
| Section | 11 Theoretical Developments | |
| DOI | https://doi.org/10.1051/epjconf/201817511009 | |
| Published online | 26 March 2018 | |
https://doi.org/10.1051/epjconf/201817511009
Atiyah-Patodi-Singer index theorem for domain-wall fermion Dirac operator
Department of Physics, Osaka University, 1-1 Machikaneyama-cho, Toyonaka, 560-0043, Osaka, JAPAN
** Speaker, e-mail: onogi@phys.sci.osaka-u.ac.jp
Published online: 26 March 2018
Recently, the Atiyah-Patodi-Singer(APS) index theorem attracts attention for understanding physics on the surface of materials in topological phases. Although it is widely applied to physics, the mathematical set-up in the original APS index theorem is too abstract and general (allowing non-trivial metric and so on) and also the connection between the APS boundary condition and the physical boundary condition on the surface of topological material is unclear. For this reason, in contrast to the Atiyah-Singer index theorem, derivation of the APS index theorem in physics language is still missing. In this talk, we attempt to reformulate the APS index in a "physicist-friendly" way, similar to the Fujikawa method on closed manifolds, for our familiar domain-wall fermion Dirac operator in a flat Euclidean space. We find that the APS index is naturally embedded in the determinant of domain-wall fermions, representing the so-called anomaly descent equations.
© The Authors, published by EDP Sciences, 2018
This is an Open Access article distributed under the terms of the Creative Commons Attribution License 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (http://creativecommons.org/licenses/by/4.0/).
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.