The Swampland at Large Number of Space-Time Dimensions

TL;DR

This paper explores swampland constraints in high-dimensional spacetimes, analyzing Kaluza-Klein spectra and proposing a new conjecture that bounds space-time dimensions based on compactification and black hole entropy behaviors.

Contribution

It introduces a novel large dimension conjecture relating KK spectra and space-time bounds, extending swampland ideas to high-dimensional contexts.

Findings

KK spectra depend on the number of dimensions D

Proposed a new conjecture limiting space-time dimensions

Black hole entropy shows similar D-dependence as KK spectra

Abstract

We discuss some aspects of swampland constraints - especially the swampland distance conjecture - in a large number of space-time dimensions $D$. We analyze Kaluza-Klein (KK) states at large $D$ and find that some KK spectra possess an interesting dependence on $D$. On the basis of these observations we propose a new large dimension conjecture. We apply it to KK states of compactifications to anti-de Sitter backgrounds where it predicts an upper bound on the dimension of space-time as a function of its characteristic radius. We also apply our conjecture to black hole spacetimes, whose entropies have a $D$-dependence very similar to that of the KK spectrum.