The Dark Dimension and the Swampland

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 $l\sim {\Lambda }^{-\frac{1}{4}}\sim 10^{-6}m$, 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 $m_{\nu }\sim ⟨H{⟩}^2{\Lambda }^{-\frac{1}{12}}{M}_{pl}^{-\frac{2}{3}}$. 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 $⟨H⟩\sim {\Lambda }^{\frac{1}{6}}{M}_{pl}^{\frac{1}{3}}$. Another prediction of the scenario is a species scale $\hat{M}\sim {\Lambda }^{\frac{1}{12}}{M}_{pl}^{\frac{2}{3}}\sim 10^9-10^{10}GeV$, 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 $\sim 10^{11}GeV$. We also speculate about the interplay between this energy scale and the GZK limit on ultra-high energy cosmic rays.

13 pages + refs; 2 figures. v2: further details and references added; v3: Published version

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