Constraining Neutrino Masses, the Cosmological Constant and BSM Physics from the Weak Gravity Conjecture

Abstract

It is known that there are AdS vacua obtained from compactifying the SM to 2 or 3 dimensions. The existence of such vacua depends on the value of neutrino masses through the Casimir effect. Using the Weak Gravity Conjecture, it has been recently argued by Ooguri and Vafa that such vacua are incompatible with the SM embedding into a consistent theory of quantum gravity. We study the limits obtained for both the cosmological constant ${\Lambda }_4$ and neutrino masses from the absence of such dangerous 3D and 2D SM AdS vacua. One interesting implication is that ${\Lambda }_4$ is bounded to be larger than a scale of order $m_{\nu }^4$, as observed experimentally. Interestingly, this is the first argument implying a non-vanishing ${\Lambda }_4$ only on the basis of particle physics, with no cosmological input. Conversely, the observed ${\Lambda }_4$ implies strong constraints on neutrino masses in the SM and also for some BSM extensions including extra Weyl or Dirac spinors, gravitinos and axions. The upper bounds obtained for neutrino masses imply (for fixed neutrino Yukawa and ${\Lambda }_4$) the existence of upper bounds on the EW scale. In the case of massive Majorana neutrinos with a see-saw mechanism associated to a large scale $M\simeq 10^{10-14}$ GeV and $Y_{{\nu }_1}\simeq 10^{-3}$, one obtains that the EW scale cannot exceed $M_{EW}\lesssim 10^2-10^4$ GeV. From this point of view, the delicate fine-tuning required to get a small EW scale would be a mirage, since parameters yielding higher EW scales would be in the swampland and would not count as possible consistent theories. This would bring a new perspective into the issue of the EW hierarchy.

41 pages, 21 figures, 5 tables. v2: Added section 6 + fig.12 + references; typos corrected

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Cited by in corpus (32)

• The Swampland: Introduction and Review
• Lectures on the Swampland Program in String Compactifications
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• Aspects of the Dark Dimension in Cosmology
• Weak Gravity Conjecture from Conformal Field Theory: A Challenge from Hyperscaling Violating and Kerr-Newman-AdS Black Holes
• One-loop running of dimension-six Higgs-neutrino operators and implications of a large neutrino dipole moment
• Quantum aspects of chaos and complexity from bouncing cosmology: A study with two-mode single field squeezed state formalism
• Swampland Constraints on Neutrino Masses
• Vacuum Energy Density Measured from Cosmological Data
• Probing Pseudo-Dirac Neutrinos with Astrophysical Sources at IceCube
• Type IIB flux compactifications with $h^{1,1}=0$
• Modular Curves and the Refined Distance Conjecture
• The Geometric $\nu$SMEFT: Operators and Connections
• Relic neutrino decay solution to the excess radio background
• Pseudo-Dirac Neutrinos and Relic Neutrino Matter Effect on the High-energy Neutrino Flavor Composition
• Extra dimensions with light and heavy neutral leptons: An application to CE$\nu$NS
• Fermion masses and mixings in the supersymmetric Pati-Salam landscape from Intersecting D6-Branes
• Axion species scale and axion weak gravity conjecture-like bound
• Fluctuating Ensemble Averages and the BTZ Threshold
• Radiative stability of tiny cosmological constant from the Swampland and quantized compactification
• AdS Swampland Conjectures and Light Fermions
• 4D dS vacua from AdS vacua of type IIB string theory and AdS distance conjecture
• Hitchhiker's Guide to the Swampland: The Cosmologist's Handbook to the string-theoretical Swampland Programme
• Further swampland constraint on Dirac Neutrino
• Confinement from Distance in Metric Space and its Relation to Cosmological Constant
• Weighing the Vacuum Energy
• Fermion Masses and Mixings in String Theory with Dirac Neutrinos
• Searching for a Dark Dimension Right-handed Neutrino in KATRIN
• The Cosmological Constant, Dark Matter and the ElectroWeak Scale meet in the Swampland
• Species scale associated with Weinberg operator and bound on Majorana neutrino mass