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Dark dimension and the grand unification of forces

Jonathan J. Heckman1,2,*, Cumrun Vafa3,†, Timo Weigand4,‡, and Fengjun Xu5,§

  • *jheckman@sas.upenn.edu
  • †vafa@g.harvard.edu
  • ‡timo.weigand@desy.de
  • §xufengjun321@gmail.com
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Phys. Rev. D 111, 046014 – Published 10 February, 2025

DOI: https://doi.org/10.1103/PhysRevD.111.046014

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 grand unified theory (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, MGUT≲1016  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∼(1–10  TeV)−1 ending on gauge branes of the same diameter ∼L. This leads to a mass of MX∼1015–1016  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 ∼1/L near a TeV and the GUT scale ∼M52L at 1016  GeV.

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Phys. Rev. D 111, 046014– Published 10 February, 2025
  • Received 19 December 2024
  • Accepted 22 January 2025
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