Consistency with quantum gravity implies constraints on the charges and masses of the physical spectra, as well as in the scalar potential of EFTs. Recently, there has been progress on sharpening these constraints when referring both to the masses of towers and to the scalar potential in the asymptotic regions of the field space. I will explain how the Distance and the deSitter conjecture can be formulated as a convex hull condition for the scalar charge to mass ratio for particles and membranes, respectively, analogous to the Weak Gravity Conjecture. This allows us to provide a quantitative and sharp bound that can be tested in string compactifications, and that can be used to re-derive global information about the moduli space and the possible duality frames. I will also show how it can be used to understand the difficulties to get scale separation in AdS as well as asymptotic accelerated expansion for runaway positive potentials.

CERN