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 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 4 ν , 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 10 10−14 GeV and Y ν 1 10 −3 , one obtains that the EW scale cannot exceed M EW 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.

AdS-phobia, the WGC, the Standard Model and Supersymmetry

“…It has been recently pointed out that AdS-phobia, if applied to the SM, would have important implications on SM physics [33,39,40]. The point is that, as described in [41], compactifying the SM to 3 or 2 dimensions one may obtain AdS vacua, depending on the values of the cosmological constant Λ 4 and the neutrino masses.…”

“…On the other hand the assumption of background independence implies that if a theory is consistent in 4D, all of its compactifications should be consistent also, since we have only changed the background geometry. Thus the existence of these lower dimensional AdS vacua (if stable) would imply the inconsistency of the SM itself [33,39]. A detailed analysis of these constraints on neutrino masses and the cosmological constant was presented in [39].…”

“…Thus the existence of these lower dimensional AdS vacua (if stable) would imply the inconsistency of the SM itself [33,39]. A detailed analysis of these constraints on neutrino masses and the cosmological constant was presented in [39]. Four interesting conclusions were obtained by imposing the absence of AdS minima,…”

“…• The lightest neutrino mass is bounded as m ν 1 ≤ 4 × 10 −3 eV (normal hierarchy) or m ν 3 ≤ 1 × 10 −3 eV (inverted hierarchy) [39].…”

“…• The cosmological constant Λ 4 is bounded from below by the mass of the lightest (Dirac) neutrino, Λ 4 m 4 ν i [39]. 1 There are examples of non-SUSY theories with AdS/CFT duals but, unlike the SM coupled to gravity, there are infinite towers of higher spin particles and do not correspond to ordinary Einstein gravity with a finite number of fields, see e.g.…”