Deviations from the $1/r^2$ Newton law due to extra dimensions

TL;DR

This paper investigates how extra dimensions modify Newton's inverse-square law, deriving Yukawa-type corrections with specific strengths and ranges based on different compactification geometries.

Contribution

It systematically calculates the strength and range of Yukawa corrections to gravity arising from various compactification schemes of extra dimensions.

Findings

Yukawa potential range is set by the lightest Kaluza-Klein mode wavelength.

Strength of correction depends on the geometry: 2n for n-torus, n+1 for n-sphere.

Maximum strength for Calabi-Yau compactifications is 20.

Abstract

We systematically examine corrections to the gravitational inverse square law, which are due to compactified extra dimensions. We find the induced Yukawa-type potentials for which we calculate the strength \alpha and range. In general the range of the Yukawa correction is given by the wavelength of the lightest Kaluza-Klein state and its strength, relative to the standard gravitational potential, by the corresponding degeneracy. In particular, when n extra dimensions are compactified on an n-torus, we find that the strength of the potential is \alpha=2n, whereas the compactification on an n-sphere gives \alpha= n+1. For Calabi-Yau compactifications the strength can be at most \alpha=20.