No-Go Theorems on Localization of Gravity around Higher Codimensional Branes in Noncompact Extra Dimensions

TL;DR

This paper demonstrates that in many gravity models, localizing massless gravity on higher codimension branes with noncompact extra dimensions is fundamentally impossible, highlighting limitations of certain brane world scenarios.

Contribution

It proves no-go theorems showing the impossibility of gravity localization for higher codimension branes with noncompact extra dimensions under broad conditions.

Findings

Localization of massless gravity fails for codimension-2 branes with noncompact extra dimensions.

Localization is also impossible for higher codimension branes with two or more noncompact extra dimensions.

The results hold under mild assumptions on field backgrounds.

Abstract

We study the brane world scenario of a single brane (or a single stack of branes) with codimension higher than one. When the extra dimensions are not small, localization of gravity around the brane is needed in order to reproduce the observable four-dimensional gravity. We focus on the case of noncompact extra dimensions, where the possibility of localized gravity becomes non-trivial. We show that in large class of gravity models, localization of massless gravity is not possible for codimension-2 branes with at least one noncompact extra dimension. With additional mild assumptions on field backgrounds, we also show that it is not possible for higher codimensional branes with two or more noncompact extra dimensions.