Abstract

Motivated by principles from the Swampland program, which characterize requirements for a consistent UV completion of quantum gravity, combined with observational data, we are led to a unique corner of the quantum gravity landscape. In particular, using the Distance/Duality conjecture and the smallness of dark energy, we predict the existence of a light tower of states and a unique extra mesoscopic dimension of length lsim {Lambda}^{-frac{1}{4}}sim {10}^{-6}m , with extra massless fermions propagating on it. This automatically leads to a candidate for a tower of sterile neutrinos, and an associated active neutrino mass scale {m}_{nu}sim {leftlangle Hrightrangle}^2{Lambda}^{-frac{1}{12}}{M}_{textrm{pl}}^{-frac{2}{3}} . Moreover, assuming the mechanism for stabilization of this dark dimension leads to similar masses for active and sterile neutrinos we are led to the prediction of a Higgs vev leftlangle Hrightrangle sim {Lambda}^{frac{1}{6}}{M}_{textrm{pl}}^{frac{1}{3}} . Another prediction of the scenario is a species scale hat{M}sim {Lambda}^{frac{1}{12}}{M}_{textrm{pl}}^{frac{2}{3}}sim {10}^9hbox{--} {10}^{10} GeV, corresponding to the higher-dimensional Planck scale. This energy scale may be related to the resolution of the instability of the Higgs effective potential present at a scale of ~1011 GeV. We also speculate about the interplay between this energy scale and the GZK limit on ultra-high energy cosmic rays.

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