Journal of High Energy Physics

, 2017:66 | Cite as

Constraining neutrino masses, the cosmological constant and BSM physics from the weak gravity conjecture

  • Luis E. Ibáñez
  • Víctor Martín-Lozano
  • Irene Valenzuela
Open Access
Regular Article - Theoretical Physics


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 Λ4 and neutrino masses from the absence of such dangerous 3D and 2D SM AdS vacua. One interesting implication is that Λ4 is bounded to be larger than a scale of order m ν 4 , as observed experimentally. Interestingly, this is the first argument implying a non-vanishing Λ4 only on the basis of particle physics, with no cosmological input. Conversely, the observed Λ4 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 Λ4) 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 ≃ 1010 − 14 GeV and Yν1 ≃ 10−3, one obtains that the EW scale cannot exceed MEW ≲ 102 − 104 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.


Beyond Standard Model Models of Quantum Gravity Quark Masses and SM Parameters Superstring Vacua 


Open Access

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Copyright information

© The Author(s) 2017

Authors and Affiliations

  • Luis E. Ibáñez
    • 1
  • Víctor Martín-Lozano
    • 2
  • Irene Valenzuela
    • 3
    • 4
  1. 1.Departamento de Física Teórica and Instituto de Física Teórica UAM/CSICUniversidad Autónoma de MadridMadridSpain
  2. 2.Bethe Center for Theoretical Physics & Physikalisches Institut der Universität BonnBonnGermany
  3. 3.Max Planck Institute for PhysicsMunichGermany
  4. 4.Institute for Theoretical Physics and Center for Extreme Matter and Emergent PhenomenaUtrecht UniversityUtrechtThe Netherlands

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