Universal Aspects of Gravity Localized on Thick Branes

TL;DR

The paper develops a universal framework for gravity localization on thick branes, showing that a normalizable graviton zero-mode guarantees four-dimensional gravity while continuum KK modes decouple at long distances, producing calculable corrections to Newton’s law that depend on the asymptotic fall-off of the background metric. It derives a Schrödinger-type equation for gravitational fluctuations in conformally-flat backgrounds and identifies the zero-mode and its normalizability criterion; extensions to non-conformally-flat cases are also provided. The authors explore thick three-branes and thick intersecting branes, demonstrate how a single scalar field can generate thick branes in five dimensions via BPS-type relations, and show that higher-dimensional intersecting backgrounds generally require more than one scalar. They discuss resonant KK modes, provide explicit example backgrounds, and present solvable constructions to illustrate localization on intersections, offering a broad, model-independent understanding of gravity in smooth brane worlds with potential phenomenological implications.

Abstract

We study gravity in backgrounds that are smooth generalizations of the Randall-Sundrum model, with and without scalar fields. These generalizations include three-branes in higher dimensional spaces which are not necessarily Anti-de Sitter far from the branes, intersecting brane configurations and configurations involving negative tension branes. We show that under certain mild assumptions there is a universal equation for the gravitational fluctuations. We study both the graviton ground state and the continuum of Kaluza-Klein modes and we find that the four-dimensional gravitational mode is localized precisely when the effects of the continuum modes decouple at distances larger than the fundamental Planck scale. The decoupling is contingent only on the long-range behaviour of the metric from the brane and we find a universal form for the corrections to Newton's Law. We also comment on the possible contribution of resonant modes. Given this, we find general classes of metrics which maintain localized four-dimensional gravity. We find that three-brane metrics in five dimensions can arise from a single scalar field source, and we rederive the BPS type conditions without any a priori assumptions regarding the form of the scalar potential. We also show that a single scalar field cannot produce conformally-flat locally intersecting brane configurations or a p-brane in greater than (p+2)-dimensions.

Figures (6)

• Figure 1: The Schrödinger potential \ref{['schpot']} for the case $A(z)=\log(k^2z^2+1)$.
• Figure 2: The shape of the potential \ref{['V2']}.
• Figure 3: The volcano box potential.
• Figure 4: Resonance of transmission $T$ into well with Kaluza-Klein mass $m$.
• Figure 5: The Schrödinger potential $V(z_1,z_2)$ for the metric \ref{['mdrsmetric']} with $k=1$ and $|z|\to z\,\tanh(10z)$.