Non-standard compactifications with mass gaps and Newton's law

TL;DR

The paper embeds 4D Minkowski space on a three-brane within 5D gauged supergravity backgrounds derived from continuous D3-brane distributions (disc and sphere). It analyzes graviton fluctuations to show a normalizable massless mode and a genuine mass gap (or discrete spectrum) above it, enabling a consistent 4D EFT on the brane. It then computes Yukawa-type corrections to Newton’s law arising from massive gravitons and demonstrates how model parameters can be chosen so these corrections remain within experimental bounds, with two illustrative regimes: (i) a mm-scale curvature scenario with potentially observable deviations, and (ii) a TeV-scale scenario where corrections are negligibly small due to wavefunction suppression. These results connect string-theoretic brane setups to phenomenologically viable 4D gravity and provide a controlled framework for assessing gravity modifications in higher-dimensional backgrounds.

Abstract

The four-dimensional Minkowski space-time is considered as a three-brane embedded in five dimensions, using solutions of five-dimensional supergravity. These backgrounds have a string theoretical interpretation in terms of D3-brane distributions. By studying linear fluctuations of the graviton we find a zero-mode representing the massless graviton in four-dimensional space-time. The novelty of our models is that the graviton spectrum has a genuine mass gap (independent of the position of the world-brane) above the zero-mode or it is discrete. Hence, an effective four-dimensional theory on a brane that includes the massless graviton mode is well defined. The gravitational force between point particles deviates from the Newton law by Yukawa-type corrections, which we compute explicitly. We show that the parameters of our solutions can be chosen such that these corrections lie within experimental bounds.