Note on solitons in brane worlds

We obtain the zero-mode effective action for gravitating objects in the bulk of dilatonic domain walls. Without additional fields included in the bulk action, the zero-mode effective action reproduces the action in one lower dimension obtained through ordinary Kaluza-Klein (KK) compactification, only when the transverse (to the domain wall) component of the bulk metric does not have a nontrivial term depending on the domain wall world volume coordinates and the tension of the domain wall is positive. With additional fields included in the bulk action, a nontrivial dependence of the transverse metric component on the domain wall longitudinal coordinates appears to be essential in reproducing the lower-dimensional action obtained via ordinary KK compactification. We find, in particular, that the effective action for the charged (p + 1)-brane in the domain wall bulk reproduces the action for the p-brane in one lower dimension.