  We carry out a numerical simulation of a domain-wall model in (4+1)
dimensions, in the presence of a quenched U(1) dynamical gauge field only in an
extra dimension, corresponding to the weak coupling limit of a (4-dimensional)
physical gauge coupling. Our numerical data suggest that the zero mode seems
absent in the symmetric phase, so that it is difficult to construct a lattice
chiral gauge theory in the continuum limit.
