Dark dimension and the grand unification of forces

Journal Article · 10 February 2025 · Physical Review. D.

DOI: https://doi.org/10.1103/PhysRevD.111.046014 · OSTI ID:2513931

Heckman, Jonathan J. ; Vafa, Cumrun; Weigand, Timo ; Xu, Fengjun

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, $M_{\mathrm{GUT}}\lesssim {10}^{16}\mathrm{GeV}$ . 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 $L\sim (1–10\mathrm{TeV}{)}^{-1}$ ending on gauge branes of the same diameter $\sim L$ . This leads to a mass of $M_X\sim {10}^{15}–{10}^{16}\mathrm{GeV}$ . 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 the GUT scale $\sim M_5^{2}L$ at ${10}^{16}\mathrm{GeV}$ . Published by the American Physical Society 2025

• Sponsoring Organization: USDOE
• Grant/Contract Number: SC0013528
• OSTI ID: 2513931
• Journal Information: Physical Review. D., Journal Name: Physical Review. D. Journal Issue: 4 Vol. 111; ISSN PRVDAQ; ISSN 2470-0010
• Publisher: American Physical SocietyCopyright Statement
• Country of Publication: United States
• Language: English