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The Atiyah-Patodi-Singer index and domain-wall fermion Dirac operators

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arxiv 1910.01987 v3 pith:DLYXHDWI submitted 2019-10-04 math.DG hep-lathep-th

Hidenori Fukaya , Mikio Furuta , Shinichiroh Matsuo , Tetsuya Onogi , Satoshi Yamaguchi , Mayuko Yamashita This is my paper · ORCID
classification math.DGhep-lathep-th
keywords atiyah-patodi-singerdomain-wallindexboundaryconditionderivationdiracedge
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We introduce a mathematician-friendly formulation of the physicist-friendly derivation of the Atiyah-Patodi-Singer index of our previous paper. Our viewpoint sheds some new light on the interplay among the Atiyah-Patodi-Singer boundary condition, domain-wall fermions, and edge modes.

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  1. $\eta$ invariant of massive Wilson Dirac operator and the index

    hep-lat 2025-01 conditional novelty 4.0 of 10

    The massive Wilson Dirac operator's eta invariant equals the continuum Dirac index on flat tori at sufficiently small lattice spacing, via K-theory.

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