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The index theorem of lattice Wilson--Dirac operators via higher index theory
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We give a proof of the index theorem of lattice Wilson--Dirac operators, which states that the index of a twisted Dirac operator on the standard torus is described in terms of the corresponding lattice Wilson--Dirac operator. Our proof is based on the higher index theory of almost flat vector bundles.
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$\eta$ invariant of massive Wilson Dirac operator and the index
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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