Self-gravity of Brane Worlds: A New Hierarchy Twist

TL;DR

This paper explores how including brane self-gravity in higher-dimensional models can naturally generate the hierarchy between the Planck scale and lower fundamental scales without large extra dimensions, offering a new perspective on the hierarchy problem.

Contribution

It introduces a novel brane-world scenario where self-gravity induces a warped geometry, providing an alternative to existing models like ADD and RS1 for explaining the hierarchy.

Findings

Gravity on the brane can become very weak due to self-gravity effects.

The hierarchy can be generated by the ratio of brane tension to brane thickness.

No issues arise with field propagation even for very thin branes.

Abstract

We examine the inclusion of brane self-gravity in brane-world scenarios with three or more compact extra dimensions. If the brane is a thin, localized one, then we find that the geometry in its vicinity is warped in such a way that gravity on the brane can become very weak, independently of the volume of the extra dimensions. As a consequence, self-gravity can make the brane structure enter into the determination of the hierarchy between the Planck scale and a lower fundamental scale. In an extreme case, one can obtain a novel reformulation of the hierarchy problem in brane worlds, without the need for large-size extra dimensions; the hierarchy would be generated when the ratio between the scales of brane tension and brane thickness is large. In a sense, such a scenario is half-way between the one of Arkani-Hamed et al.(ADD) (although with TeV-mass Kaluza-Klein states) and that of Randall and Sundrum (RS1) (but with only a TeV brane, and of positive tension). We discuss in detail the propagation of fields in the background of this geometry, and find that no problems appear even if the brane is taken to be very thin. We also discuss the presence of black branes and black holes in this setting, and the possibility of having a Planck brane.