Consistency Conditions for Brane Worlds in Arbitrary Dimensions

TL;DR

This paper derives consistency conditions for brane world models across various dimensions, revealing that negative tension branes are required in five dimensions but can be avoided in higher dimensions, exemplified by a six-dimensional model with only positive tension branes.

Contribution

It generalizes brane world sum rules to arbitrary dimensions and presents a new six-dimensional model with positive tension branes avoiding previous constraints.

Findings

Negative tension branes are necessary in 5D models.

In higher dimensions, positive tension branes can satisfy consistency conditions.

A novel 6D Randall--Sundrum model with only positive tension branes is proposed.

Abstract

We consider ``brane world sum rules'' for compactifications involving an arbitrary number of spacetime dimensions. One of the most striking results derived from such consistency conditions is the necessity for negative tension branes to appear in five--dimensional scenarios. We show how this result is easily evaded for brane world models with more than five dimensions. As an example, we consider a novel realization of the Randall--Sundrum scenario in six dimensions involving only positive tension branes.