A physicist-friendly reformulation of the mod-two Atiyah-Patodi-Singer index

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...

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Published inarXiv.org
Main Authors Fukaya, Hidenori, Furuta, Mikio, Matsuki, Yoshiyuki, Matsuo, Shinichiroh, Onogi, Tetsuya, Yamaguchi, Satoshi, Yamashita, Mayuko
Format Paper
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 22.11.2021
Subjects
Boundary conditions
Domain walls
Fermions
Formalism
Invariants
Partitions (mathematics)
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Summary: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.
ISSN:2331-8422