Dark dimension and the grand unification of forces
Jonathan J. Heckman (Department of Physics and Astronomy, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA, Department of Mathematics, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA); Cumrun Vafa (Jefferson Physical Laboratory, Harvard University, Cambridge, Massachusetts 02138, USA); Timo Weigand (II. Institut für Theoretische Physik, Universität Hamburg, Luruper Chaussee 149, 22761 Hamburg, Germany); Fengjun Xu (Beijing Institute of Mathematical Sciences and Applications (BIMSA), Beijing 101408, China)
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, . Combined with the experimental bound on the proton lifetime, this predicts that the gauge boson mediating proton decay is a 5D solitonic string of Planckian tension stretched across a length scale ending on gauge branes of the same diameter . This leads to a mass of . 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 of the gauge branes correlates with both the weak scale near a TeV and the GUT scale at .