Our World as an Intersection of Walls and a String

TL;DR

This paper derives a solution to Einstein's equations for our four-dimensional universe as an intersection of a wall and a string-like defect in seven-dimensional spacetime, analyzing gravity localization and potential corrections.

Contribution

It presents a novel higher-dimensional model of our universe as an intersection of defects and studies the localization of gravity and corrections to Newton's law.

Findings

A massless graviton is localized at the intersection.

The correction to Newton's potential resembles that of a five-dimensional wall.

Generalization to multiple intersecting walls yields similar gravitational results.

Abstract

A solution of Einstein equations is obtained for our four-dimensional world as an intersection of a wall and a string-like defect in seven-dimensional spacetime with a negative cosmological constant. A matter energy-momentum tensor localized on the wall and on the string is needed. A single massless graviton is found and is localized around the intersection. The leading correction to the gravitational Newton potential from massive spin 2 graviton is found to be almost identical to that of a wall in five dimensions, contrary to the case of a string in six dimensions. The generalization to the intersection of a string and $n$ orthogonally intersecting walls is also obtained and a similar result is found for the gravitational potential.