Effective Equations on the 3-Brane World from Type IIB String

TL;DR

This paper derives effective equations for a 3-brane in a type IIB string theory setting, incorporating bulk fields and geometric interactions, extending previous gravity-only models to include string-derived matter fields.

Contribution

It extends the derivation of effective brane equations to include bulk fields from type IIB string theory using a geometric approach with Einstein-Cartan space.

Findings

Effective equations incorporate bulk string fields.

Interactions are described geometrically without extra assumptions.

Equations are expressed in Riemannian terms.

Abstract

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 effective equations on the 3-brane, where only gravity penetrates in the bulk has been performed by Shiromizu, Maeda, and Sasaki. We extend this analysis 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 have expressed completely in Riemannian terms and make conclusions.