Mod-two APS index and domain-wall fermion
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.
- Publication:
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arXiv e-prints
- Pub Date:
- December 2020
- DOI:
- 10.48550/arXiv.2012.03543
- arXiv:
- arXiv:2012.03543
- Bibcode:
- 2020arXiv201203543F
- Keywords:
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- High Energy Physics - Theory;
- High Energy Physics - Lattice;
- Mathematics - Differential Geometry
- E-Print:
- 30 pages, 1 figure, minor corrections