A physicist-friendly reformulation of the mod-two Atiyah-Patodi-Singer index
Abstract
Gauge anomaly in 4-dimensions can be viewed as a current inflow into an extra-dimension, where the total phase of the fermion partition function is given in a gauge invariant way by the Atiyah- Patodi-Singer(APS) eta-invariant of a 5-dimensional Dirac operator. However, this formalism requires a non-local boundary condition, with which the physical roles of edge/bulk modes are unclear and how the causality of the theory is maintained is not obvious. In this work, we consider a special case where the Dirac operator is in a real representation and its eta invariant becomes the mod-two type APS index. We propose a physicist-friendly reformulation of the mod-two index using domain-wall fermion formalism, which naturally describes how the global anomaly is canceled between edge and bulk.
Keywords
Cite
@article{arxiv.2111.11040,
title = {A physicist-friendly reformulation of the mod-two Atiyah-Patodi-Singer index},
author = {Hidenori Fukaya and Mikio Furuta and Yoshiyuki Matsuki and Shinichiroh Matsuo and Tetsuya Onogi and Satoshi Yamaguchi and Mayuko Yamashita},
journal= {arXiv preprint arXiv:2111.11040},
year = {2021}
}
Comments
10 pages, 1 figure, talk presented at the 38th International Symposium on Lattice Field Theory (LATTICE2021); to appear in Proceedings of Science, PoS(LATTICE2021)617