The index of a Ginsparg-Wilson Dirac operator

A novel feature of a Ginsparg-Wilson lattice Dirac operator is discussed. U nlike the Dirac operator for massless fermions in the continuum, this latti ce Dirac operator does not possess topological zero modes for any topologic ally-nontrivial background gauge fields, even though it is exponentially-lo cal, doublers-free, and reproduces correct axial anomaly for topologically- trivial gauge configurations. (C) 2001 Elsevier Science B.V. All rights res erved.