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arXiv · 2012.03543

Mod-two APS index and domain-wall fermion

Hidenori Fukaya·Mikio Furuta·Yoshiyuki Matsuki·Shinichiroh Matsuo·Tetsuya Onogi·Satoshi Yamaguchi·Mayuko Yamashita
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Abstract

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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Hidenori Fukaya, Mikio Furuta, Yoshiyuki Matsuki, Shinichiroh Matsuo, Tetsuya Onogi, Satoshi Yamaguchi, Mayuko Yamashita. 2020-12-07. Mod-two APS index and domain-wall fermion. https://arxiv.org/abs/2012.03543

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