Localization of matter fields and non-Abelian gauge fields on domain walls

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.