Locality bound for effective four-dimensional action of domain-wall fermion

We discuss locality in the domain-wall QCD through the effective four-dimensional Dirac operator which is defined by the transfer matrix of the five-dimensional Wilson fermion. We first derive an integral representation for the effective operator, using the inverse five-dimensional Wilson-Dirac operator with the anti-periodic boundary condition in the fifth direction. Exponential bounds are obtained from it for gauge fields with small lattice field strength.