Perturbation calculation of the axial anomaly of a Ginsparg-Wilson lattice Dirac operator

A recent proposal suggests that even if a Ginsparg-Wilson lattice Dirac operator does not possess any topological zero modes in topologically nontrivial gauge backgrounds, it can reproduce the correct axial anomaly for sufficiently smooth gauge configurations, provided that it is exponentially local, doubler-free, and has the correct continuum behavior. In this paper, we calculate the axial anomaly of this lattice Dirac operator in weak coupling perturbation theory, and show that it recovers the topological charge density in the continuum limit.