Alice in Warpland: KK modes, Warped Compactifications and the Swampland

TL;DR

This paper analyzes how warping affects the asymptotic behavior of Kaluza-Klein towers in warped compactifications, revealing a link between the Sharpened Distance Conjecture and higher-dimensional de Sitter conditions.

Contribution

It provides explicit solutions for KK mass decay rates in warped backgrounds and connects these results to swampland conjectures and de Sitter conditions.

Findings

Warping reduces the exponential decay rate of KK masses.

Strong warping can potentially violate the Sharpened Distance Conjecture bound.

The Sharpened Distance Conjecture aligns with the absence of asymptotic accelerated expansion.

Abstract

We investigate the asymptotic behavior of Kaluza-Klein (KK) towers in warped compactifications to Minkowski space. Focusing on the overall decompactification limit, we derive the scaling of KK masses at large KK momentum for scalar fluctuations in lower-dimensional Planck units. In codimension-one warped backgrounds sourced by a higher-dimensional exponential potential, we solve explicitly for the internal profiles and obtain a closed expression for the exponential mass decay rate $\lambda_{\rm KK}$ of the tower in terms of the moduli space distance. We find that warping reduces $\lambda_{\rm KK}$ relative to the unwarped case, in such a way that sufficiently strong warping could in principle violate the Sharpened Distance Conjecture bound. Remarkably, this sharpened bound is still satisfied precisely when the higher-dimensional potential obeys the condition forbidding asymptotic accelerated expansion, establishing a direct link between the Sharpened Distance Conjecture and the Strong de Sitter condition in one higher dimension. We also argue that for higher-codimension warped backgrounds the asymptotic KK scaling remains unmodified.