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High Energy Physics - Theory

arXiv:2111.11040 (hep-th)
[Submitted on 22 Nov 2021]

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

Authors:Hidenori Fukaya, Mikio Furuta, Yoshiyuki Matsuki, Shinichiroh Matsuo, Tetsuya Onogi, Satoshi Yamaguchi, Mayuko Yamashita
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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.
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
Subjects: High Energy Physics - Theory (hep-th); High Energy Physics - Lattice (hep-lat); Mathematical Physics (math-ph)
Report number: OU-HET-1120
Cite as: arXiv:2111.11040 [hep-th]
  (or arXiv:2111.11040v1 [hep-th] for this version)
  https://doi.org/10.48550/arXiv.2111.11040

Submission history

From: Yoshiyuki Matsuki [view email]
[v1] Mon, 22 Nov 2021 08:04:02 UTC (798 KB)
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