  Both non-Abelian gauge fields and minimally interacting massless matter
fields are localized on a domain wall in the five-dimensional spacetime.
Field-dependent gauge coupling naturally gives a position-dependent coupling to
localize non-Abelian gauge fields on the domain wall. An economical field
content allows us to eliminate a moduli for a instability, and to demonstrate
the positivity of the position-dependent coupling in the entire moduli space.
Effective Lagrangian similar to the chiral Lagrangian is found with a new
feature of different coupling strengths for adjoint and singlet matter that
depend on the width of the domain wall.
