Consistency with quantum gravity can have significant consequences on low energy physics. For instance, using the Weak Gravity Conjecture, it has been recently argued by Ooguri and Vafa that non supersymmetric stable AdS vacua are incompatible with quantum gravity. However, it is known that AdS vacua can appear from compactifying the Standard Model to 2 or 3 dimensions. By requiring the absence of these vacua we can put constraints on the SM and BSM spectra, obtaining a lower bound for the cosmological constant in terms of the neutrino masses. This can also be translated into an upper bound for the EW scale around the TeV range, bringing a new perspective into the issue of the EW hierarchy.