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arxiv 2012.03543 v2 pith:6FAN5AQ5 submitted 2020-12-07 hep-th hep-latmath.DG

Mod-two APS index and domain-wall fermion

Hidenori Fukaya , Mikio Furuta , Yoshiyuki Matsuki , Shinichiroh Matsuo , Tetsuya Onogi , Satoshi Yamaguchi , Mayuko Yamashita This is my paper
classification hep-th hep-latmath.DG
keywords fermionboundarydomain-wallindexmanifolddifferentgivenmod-two
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved
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We reformulate the mod-two Atiyah-Patodi-Singer (APS) index in a physicist-friendly way using the domain-wall fermion. Our new formulation is given on a closed manifold, which is extended from the original manifold with boundary, where we instead give a fermion mass term changing its sign at the location of the original boundary. This new setup does not need the APS boundary condition, which is non-local. A mathematical proof of equivalence between the two different formulations is given by two different evaluations of the same index of a Dirac operator on a higher dimensional manifold. The domain-wall fermion allows us to separate the edge and bulk mode contributions in a natural but not in a gauge invariant way, which offers a straightforward description of the global anomaly inflow.

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Cited by 3 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. Capturing the Atiyah-Patodi-Singer index from the lattice

    math.DG 2026-02 unverdicted novelty 7.0

    A lattice formulation of the Atiyah-Patodi-Singer index is built using spectral flow of domain-wall Dirac operators generalized beyond product boundaries and proven to recover the continuum index for small enough latt...

  2. Higher-Rank Orthogonal Twists, APS Boundary Conditions, and $O(2)$-Equivariant Spectral Flow on a Warped Cylinder

    math-ph 2026-06 unverdicted novelty 6.0

    Derives an explicit blockwise RO(O(2))-valued spectral flow formula for regularized APS families of Dirac operators on warped cylinders with orthogonal twists.

  3. Reflection Symmetry, APS Boundary Conditions, and Equivariant Spectral Flow on a Warped Cylinder

    math-ph 2026-05 unverdicted novelty 6.0

    Reflection symmetry on twisted Dirac operators on warped cylinders holds precisely when 2A is integer, yielding unitary equivalence of APS blocks and an RO(O(2))-valued or mod-two spectral-flow invariant.