The Atiyah–Patodi–Singer index on a lattice

Abstract We propose a nonperturbative formulation of the Atiyah–Patodi–Singer (APS) index in lattice gauge theory in four dimensions, in which the index is given by the $\eta$ invariant of the domain-wall Dirac operator. Our definition of the index is always an integer with a finite lattice spacing....

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Bibliographic Details
Published in:Progress of theoretical and experimental physics 2020-04, Vol.2020 (4)
Main Authors: Fukaya, Hidenori, Kawai, Naoki, Matsuki, Yoshiyuki, Mori, Makito, Nakayama, Katsumasa, Onogi, Tetsuya, Yamaguchi, Satoshi
Format: Article
Language:English
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Summary:Abstract We propose a nonperturbative formulation of the Atiyah–Patodi–Singer (APS) index in lattice gauge theory in four dimensions, in which the index is given by the $\eta$ invariant of the domain-wall Dirac operator. Our definition of the index is always an integer with a finite lattice spacing. To verify this proposal, using the eigenmode set of the free domain-wall fermion we perturbatively show in the continuum limit that the curvature term in the APS theorem appears as the contribution from the massive bulk extended modes, while the boundary $\eta$ invariant comes entirely from the massless edge-localized modes.
ISSN:2050-3911
2050-3911
DOI:10.1093/ptep/ptaa031