Abstract
The spectral flows of the hermitian Wilson-Dirac operator for a continuous family of abelian gauge fields connecting different topological sectors are shown to have a characteristic structure leading to the lattice index theorem. The index of the overlap Dirac operator is shown to coincide with the topological charge for a wide class of gauge field configurations. It is also argued that in two dimensions the eigenvalue spectra for some special but nontrivial background gauge fields can be described by a set of universal polynomials and the index can be found exactly.
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