  Dynamical localization of non-Abelian gauge fields in non-compact flat $D$
dimensions is worked out. The localization takes place via a field-dependent
gauge kinetic term when a field condenses in a finite region of spacetime. Such
a situation typically arises in the presence of topological solitons. We
construct four-dimensional low-energy effective Lagrangian up to the quadratic
order in a universal manner applicable to any spacetime dimensions. We devise
an extension of the $R_\xi$ gauge to separate physical and unphysical modes
clearly. Out of the D-dimensional non-Abelian gauge fields, the physical
massless modes reside only in the four-dimensional components, whereas they are
absent in the extra-dimensional components. The universality of non-Abelian
gauge charges holds due to the unbroken four-dimensional gauge invariance. We
illustrate our methods with models in $D=5$ (domain walls), in $D=6$
(vortices), and in $D=7$.
