Index of a family of lattice Dirac operators and its relation to the non-Abelian anomaly on the lattice

In the continuum, a topological obstruction to the vanishing of the non-Abe lian anomaly in 2n dimensions is given by the index of a certain Dime opera tor in 2n + 2 dimensions, or equivalently, the index of a 2-parameter famil y of Dirac operators in 2n dimensions. In this paper an analogous result is derived for chiral fermions on the lattice in the overlap formulation. Thi s involves deriving an index theorem for a family of lattice Dirac operator s satisfying the Ginsparg-Wilson relation. The index density is proportiona l to Luscher's topological field in 2n + 2 dimensions.