Overlap topological charge and axial anomaly for lattice fermions with overlap-Dirac operator

We study the classical continuum limit of the overlap topological charge Q (m) lat . For m = r = 1 , and with either periodic or anti-periodic boundary conditions on the spinor fields, we prove that Qlat reduces to the continuum topological charge Q when the continuum gauge field is in a singular gauge, vanishes outside a bounded region, and is pure gauge in a neighbourhood of the singularity. In the non-singular (Q= 0) case this result is established for general values of the parameters m and r. The calculation also determines the continuum limit of the density function for Qlat , which is seen to reproduce the density function for Q when 0 < m < 2. This can be viewed as an exact derivation of the classical continuum limit of the axial anomaly for lattice fermions with overlap-Dirac operator.