Standard 4d gravity on a brane in six dimensional flux compactifications

TL;DR

This paper demonstrates that in a six-dimensional flux compactification model with a codimension one brane, four-dimensional Einstein gravity emerges at large distances, providing a consistent framework for studying gravity in such higher-dimensional setups.

Contribution

It presents the first complete analysis of gravity in a realistic 6D brane model with flux compactification, avoiding delta-like codimension two branes and including stabilization mechanisms.

Findings

Gravity on the brane is described by Einstein 4D gravity at large scales.

The model is consistent without the complications of delta-like codimension two branes.

Stabilization of the extra dimensions is successfully incorporated.

Abstract

We consider a six dimensional space-time, in which two of the dimensions are compactified by a flux. Matter can be localized on a codimension one brane coupled to the bulk gauge field and wrapped around an axis of symmetry of the internal space. By studying the linear perturbations around this background, we show that the gravitational interaction between sources on the brane is described by Einstein 4d gravity at large distances. Our model provides a consistent setup for the study of gravity in the rugby (or football) compactification, without having to deal with the complications of a delta-like, codimension two brane. To our knowledge, this is the first complete study of gravity in a realistic brane model with two extra dimensions, in which the mechanism of stabilization of the extra space is consistently taken into account.