The massive Wilson Dirac operator's eta invariant equals the continuum Dirac index on flat tori at sufficiently small lattice spacing, via K-theory.
A lattice version of the Atiyah-Singer index theorem
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abstract
We formulate and prove a lattice version of the Atiyah-Singer index theorem. The main theorem gives a $K$-theoretic formula for an index-type invariant of operators on lattice approximations of closed integral affine manifolds. We apply the main theorem to an index problem of Wilson-Dirac operators in lattice gauge theory.
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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.