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

TL;DR

The paper investigates how the absence of stable AdS vacua arising from SM compactifications constrains infrared parameters, notably the cosmological constant $Λ_4$ and neutrino masses, via the sharpened Weak Gravity Conjecture. By calculating radion-Casimir potentials for 3D and 2D compactifications and imposing no-AdS vacua, it derives lower bounds on $Λ_4$ that scale roughly as $m_ν^4$ and translates these into upper bounds on the electroweak scale in see-saw scenarios. It also analyzes how extra light states (Weyl/Dirac fermions, gravitinos, axions) modify the bounds, sometimes restoring viability for Majorana or Dirac neutrinos, and discusses the implications for the EW hierarchy and possible axiverse scenarios. The study highlights a deep link between quantum gravity consistency and IR physics, suggesting that the observed cosmological constant and light fermions could be dictated by swampland constraints rather than cosmological inputs, with testable implications for neutrino physics and beyond-SM content.

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 $Λ_4$ and neutrino masses from the absence of such dangerous 3D and 2D SM AdS vacua. One interesting implication is that $Λ_4$ 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 $Λ_4$ only on the basis of particle physics, with no cosmological input. Conversely, the observed $Λ_4$ 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 $Λ_4$) 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 $Y_{ν_1}\simeq 10^{-3}$, 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.

Figures (21)

• Figure 1: Effective potential as a function of the radion field, R, for the cosmological constant (black) and the sum of the cosmological constant, graviton and photon contributions (red).
• Figure 2: Normal and inverted hierarchies of neutrino masses.
• Figure 3: Effective radion potential for Majorana neutrinos when considering normal hierarchy (left) and inverted hierarchy (right). In both cases the lightest neutrino is considered massless, $m_{\nu_1}=0$ for NH and $m_{\nu_3}=0$ for IH.
• Figure 4: Radion effective potential for Dirac neutrinos when considering normal hierarchy (left) and inverted hierarchy (right). For the case of NH the different lines correspond to several values for the lightest neutrino mass: $m_{\nu_1}=$ 6.0 meV (black), 6.5 meV (green), 7.0 meV (blue), 7.5 meV (brown) and 8.0 meV (red). In the case of IH the different colours correspond to the lightest neutrino masses: $m_{\nu_3}=$ 1.5 meV (black), 2.0 meV (green), 2.5 meV (blue), 3.0 meV (red).
• Figure 5: Majorana neutrinos. Lower bound on the value of the 4D cosmological constant as a function of the lightest neutrino mass coming from absence of AdS vacua. Left: NI. Right: IH.