Newton versus Coulomb for Kaluza-Klein modes

TL;DR

This paper analyzes Kaluza-Klein modes in various compactification scenarios, comparing gravitational and gauge interactions, and explores implications for the Weak Gravity Conjecture through amplitude calculations.

Contribution

It provides a detailed comparison of gravitational and gauge amplitudes in compactified theories, elucidating the interplay of interactions and constraints related to the Weak Gravity Conjecture.

Findings

Recovered known Weak Gravity Conjecture constraints

Analyzed KK mode pair-production across dimensions

Explored effects of non-minimal scalar couplings

Abstract

We consider a set of elementary compactifications of $D+1$ to $D$ spacetime dimensions on a circle: first for pure general relativity, then in the presence of a scalar field, first free then with a non minimal coupling to the Ricci scalar, and finally in the presence of gauge bosons. We compute the tree-level amplitudes in order to compare some gravitational and non-gravitational amplitudes. This allows us to recover the known constraints of the $U(1)$, dilatonic and scalar Weak Gravity Conjectures in some cases, and to show the interplay of the different interactions. We study the KK modes pair-production in different dimensions. We also discuss the contribution to some of these amplitudes of the non-minimal coupling in higher dimensions for scalar fields to the Ricci scalar.