A Note on Solitons in Brane Worlds

TL;DR

This paper derives the effective action for gravitating objects in dilatonic domain walls, showing conditions under which it matches lower-dimensional theories and exploring the role of additional bulk fields.

Contribution

It clarifies how zero mode effective actions relate to Kaluza-Klein compactification in brane world scenarios, especially with additional bulk fields.

Findings

Effective action matches lower-dimensional theory when transverse metric components are trivial.

Additional bulk fields induce non-trivial transverse metric dependence.

Charged brane effective action reproduces lower-dimensional p-brane action.

Abstract

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 dimensions obtained through the ordinary Kaluza-Klein (KK) compactification, only when the transverse (to the domain wall) component of the bulk metric does not have non-trivial term depending on the domain wall worldvolume coordinates. With additional fields included in the bulk action, non-trivial dependence of the transverse metric component on the domain wall worldvolume coordinates appears to be essential in reproducing the lower-dimensional action obtained via the 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 dimensions.