  A mechanism using the position-dependent gauge coupling is proposed to
localize non-Abelian gauge fields on domain walls in five-dimensional
space-time. Low-energy effective theory posseses a massless vector field, and a
mass gap. The four-dimensional gauge invariance is maintained intact. We obtain
perturbatively the four-dimensional Coulomb law for static sources on the
domain wall. BPS domain wall solutions with the localization mechanism are
explicitly constructed in the U(1)xU(1) supersymmetric gauge theory coupling to
the non-Abelian gauge fields only through the cubic prepotential, which is
consistent with the general principle of supersymmetry in five-dimensional
space-time.
