On Newton's law in supersymmetric braneworld models

TL;DR

This paper investigates how gravitons propagate in 5-D supersymmetric braneworld models with a bulk scalar field, revealing modifications to Newton's law at short distances that depend on the superpotential shape, with potential observable effects.

Contribution

It demonstrates that after stabilization, the bulk gravitons influence Newtonian gravity, with specific calculations for dilatonic scenarios and implications for 5-D Heterotic M-theory.

Findings

Short-distance Newtonian potential receives shape-dependent corrections.

In dilatonic models, these corrections are explicitly computed.

Potential observable effects at micron scales in certain string-inspired models.

Abstract

We study the propagation of gravitons within 5-D supersymmetric braneworld models with a bulk scalar field. The setup considered here consists of a 5-D bulk spacetime bounded by two 4-D branes localized at the fixed points of an $S^1/Z_2$ orbifold. There is a scalar field $\phi$ in the bulk which, provided a superpotential $W(\phi)$, determines the warped geometry of the 5-D spacetime. This type of scenario is common in string theory, where the bulk scalar field $\phi$ is related to the volume of small compact extra dimensions. We show that, after the moduli are stabilized by supersymmetry breaking terms localized on the branes, the only relevant degrees of freedom in the bulk consist of a 5-D massive spectrum of gravitons. Then we analyze the gravitational interaction between massive bodies localized at the positive tension brane mediated by these bulk gravitons. It is shown that the Newtonian potential describing this interaction picks up a non-trivial contribution at short distances that depends on the shape of the superpotential $W(\phi)$. We compute this contribution for dilatonic braneworld scenarios $W(\phi) = e^{\alpha \phi}$ (where $\alpha$ is a constant) and discuss the particular case of 5-D Heterotic M-theory: It is argued that a specific footprint at micron scales could be observable in the near future.