The dark dimension, proton decay, and the length of the M-theory interval

TL;DR

This paper explores how proton decay constraints limit the size of a hypothesized dark dimension in M-theory, suggesting it must be extremely small, around 10^{-28} meters, impacting cosmological and experimental models.

Contribution

It demonstrates that proton decay searches impose strict upper bounds on the size of the dark dimension in M-theory, constraining theoretical models with large extra dimensions.

Findings

The dark dimension must be smaller than approximately 10^{-28} meters.

Proton decay experiments significantly restrict the size of extra dimensions in M-theory.

The results impact cosmological models involving large extra dimensions.

Abstract

The existence of a large extra dimension in which only gravity propagates would have spectacular consequences for cosmology and laboratory experiments. In the strong coupling limit of the $E_8\times E_8$ heterotic string theory, the gauge and matter fields live at the end of the eleventh dimension, which becomes a natural candidate for a micron-size \textit{dark dimension}. In this work, however, we show that the length of the M-theory interval is severely constrained by proton decay searches. Our results indicate that in such constructions the size of the eleventh dimension is $R\lesssim \mathcal{O}(10^{-28})$ meters.