Effective equations on the 3-brane world from type IIB string

The effective field equations on a 3-brane are established considering the massless bosonic sector of the type IIB string compactified on S-5. The covariant embedding formalism in a space endowed with Z(2)-symmetry is applied. Recently the derivation of the effective equations on the 3-brane, where only gravity penetrates in the bulk was performed by Shiromizu, Maeda, and Sasaki. We extend this approach to the situation when the bulk contains a set of fields given by the type IIB string. The notion of the Einstein-Cartan space is considered in order to avoid extra suppositions about the embedding of these fields. The interactions between the brane and the bulk fields are understood in a purely geometric way, which fixes the form of these interactions. Finally, we present the dynamically equivalent effective equations expressed completely in Riemannian terms and make conclusions.