  We propose a method for simultaneous localization of non-Abelian gauge fields
and matter fields with minimal interaction on domain walls using $U(N)_c$ gauge
theory with $SU(N)_{L}\times SU(N)_{R}\times U(1)_{A}$ flavor symmetry.
Localization of non-Abelian fields is achieved using field-dependent gauge
coupling. We find that effective Lagrangian up to second order of derivatives
for low energy fluctuations resembles a chiral model from hadron physics with
additional minimal interactions of pions with localized gauge fields together
with nonlinear interactions of moduli fields. This result provides a step
towards a realistic model building of brane-world scenario using topological
solitons.
