Localizing Gravity on the Triple Intersection of 7-branes in 10D

TL;DR

This paper demonstrates how gravity can be localized on the intersection of three 7-branes in a 10-dimensional anti-de Sitter space, providing a potential model for our universe within string theory frameworks.

Contribution

It explicitly derives conditions for gravity localization on 7-brane intersections in 10D and analyzes the geometric and energetic properties involved.

Findings

Gravity can be localized on the intersection of three 7-branes in AdS10.

Derived exact relations among brane tensions independent of energy distribution.

Identified a subtlety in applying Stoke's Theorem in this setup.

Abstract

It was recently proposed that our universe could naturally come to be dominated by 3-branes and 7-branes if the universe is ten-dimensional. In this paper, we explicitly demonstrate that gravity can be localized on the intersection of three 7-branes in AdS10 to give four-dimensional gravity. We derive the exact relations among the tensions of the branes, and show that they apply independently of the precise distribution of energy within the necessarily thickened branes. We demonstrate this with several technical sections showing a simple formula for the curvature tensor of a diagonal metric with isometries as well as for the curvature at a gravitational singularity. We also demonstrate a subtlety in applying Stoke's Theorem to this set-up.