The Dark Dimension and the Grand Unification of Forces

TL;DR

This paper explores how the dark dimension scenario constrains grand unification, predicting a GUT scale below 10^{16} GeV and linking it to TeV-scale physics through Kaluza-Klein excitations and brane configurations.

Contribution

It demonstrates that grand unification in the dark dimension scenario imposes specific bounds on the GUT scale and predicts observable Kaluza-Klein modes near the TeV range.

Findings

Upper bound for GUT scale: M_GUT pprox 10^{16} GeV

Predicted tower of KK excitations in the 1-10 TeV range

Correlation between gauge brane separation and both weak and GUT scales

Abstract

The dark dimension scenario, predicting one extra mesoscopic dimension in the micron range, has emerged by applying various Swampland principles to the dark energy. In this note we find that realizing the grand unification of gauge forces is highly constraining in this context. Without actually constructing any GUT models, we argue that the mere assumption of grand unification of forces in this scenario, together with the experimental bounds on massive replicas of the Standard Model gauge bosons, predicts an upper bound for the GUT scale, $M_{GUT}\lesssim 10^{16}\ {\rm GeV}$. Combined with the experimental bound on the proton lifetime, this predicts that the $X$ gauge boson mediating proton decay is a 5d solitonic string of Planckian tension stretched across a length scale $L\sim ({\rm 1-10\ TeV})^{-1}$ ending on gauge branes of the same diameter $\sim L$. This leads to a mass of $M_X\sim 10^{15}-10^{16}\ {\rm GeV}$. In particular assuming grand unification in the dark dimension scenario results in a tower of Kaluza-Klein excitations of Standard Model gauge bosons on the gauge branes in the 1-10 TeV range. This suggests that the diameter/separation $L$ of the gauge branes correlates with both the weak scale $\sim 1/L$ near a TeV {\it and} the GUT scale $\sim M_5^2 L$ at $10^{16}\ {\rm GeV}$.