Consistency with quantum gravity can have significant consequences on low energy physics. Interestingly, it seems that not every effective field theory can be consistently coupled to quantum gravity unless it satisfies some additional consistency constraints. In this talk, I will review one of these constraints, dubbed The Weak Gravity Conjecture, with special focus on its phenomenological consequences for Particle Physics. In particular, we show that a refinement of this conjecture, when applied to compactifications of the
Standard Model, implies an upper bound for the neutrino masses in terms of the cosmological constant in our universe. Furthermore, Majorana neutrinos would only be compatible if accompanied by very light new BSM physics.
This bound can also be translated into an upper bound for the EW scale around the TeV range, bringing a new perspective into the EW hierarchy problem.