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

We discuss locality in the domain-wall QCD through the effective four-dimen sional Dirac operator which is defined by the transfer matrix of the five-d imensional Wilson fermion. We first derive an integral representation for t he effective operator, using the inverse five-dimensional Wilson-Dirac oper ator with the anti-periodic boundary condition in the fifth direction. Expo nential bounds are obtained from it for gauge fields with small lattice fie ld strength. (C) 2000 Elsevier Science B.V. All rights reserved.