The massive Wilson Dirac operator's eta invariant equals the continuum Dirac index on flat tori at sufficiently small lattice spacing, via K-theory.
The Schr\"odinger functional in lattice QCD with exact chiral symmetry
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abstract
Similarly to the interaction lagrangian, the possible boundary conditions in quantum field theories on space-time manifolds with boundaries are strongly constrained by the symmetry and scaling properties of the theory. Based on this general insight, a lattice formulation of the QCD Schr\"odinger functional is proposed for the case where the lattice Dirac operator in the bulk of the lattice coincides with the Neuberger--Dirac operator. The construction satisfies all basic requirements (locality, symmetries, hermiticity) and is suitable for numerical simulations.
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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.