Self-gravity of Brane Worlds: A New Hierarchy Twist

TL;DR

This work investigates how brane self-gravity in $4+n$ dimensions with $n\ge 3$ alters gravity on the brane and offers a novel route to the Planck-TeV hierarchy. By solving for a self-gravitating three-brane, the authors show that near-brane warping weakens four-dimensional gravity in a way controlled by the ratio $r_b/r_0$, independent of the extra-volume size, and derive a power-law relation for $G_4$ in terms of $G_{4+n}$ and $V_0$. Scalar and graviton perturbations are analyzed, revealing a dominant zero-mode on the brane that yields well-behaved, finite interactions even with a singular brane core. They also explore black brane and black hole configurations, their finite entropy in compact spaces, and potential Planck-brane realizations, highlighting a bridge between ADD-like bulk and RS-like warping. The results demonstrate a new, core-dependent mechanism to generate hierarchy and stress the importance of brane core modeling and moduli stabilization for realistic implementations.

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.

Figures (2)

• Figure 1: Plot of the potential $V=V(r)$ for $n=3$ (solid line) and $n=4$ with $r_0=0.5$
• Figure 2: Plot of massive mode wavefunctions for $n=3$, $r_0=1$.