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Both non-Abelian gauge fields and minimally interacting massless matterfields are localized on a domain wall in the five-dimensional spacetime.Field-dependent gauge coupling naturally gives a position-dependent coupling tolocalize non-Abelian gauge fields on the domain wall. An economical fieldcontent allows us to eliminate a moduli for a instability, and to demonstratethe positivity of the position-dependent coupling in the entire moduli space.Effective Lagrangian similar to the chiral Lagrangian is found with a newfeature of different coupling strengths for adjoint and singlet matter thatdepend on the width of the domain wall.

Stabilizing matter and gauge fields localized on walls