  We consider Kaplan's domain wall fermions in the presence of an Anti-de
Sitter (AdS) background in the extra dimension. Just as in the flat space case,
in a completely vector-like gauge theory defined after discretizing this extra
dimension, the spectrum contains a very light charged fermion whose chiral
components are localized at the ends of the extra dimensional interval. The
component on the IR boundary of the AdS space can be given a large mass by
coupling it to a neutral fermion via the Higgs mechanism. In this theory, gauge
invariance can be restored either by taking the limit of infinite proper length
of the extra dimension or by reducing the AdS curvature radius towards zero. In
the latter case, the Kaluza-Klein modes stay heavy and the resulting classical
theory approaches a chiral gauge theory, as we verify numerically. Potential
difficulties for this approach could arise from the coupling of the
longitudinal mode of the light gauge boson, which has to be treated
non-perturbatively.
