We analyze infrared consistency conditions of 3D and 4D effective field theories with massive scalars or fermions charged under multiple U (1) gauge fields. At low energies, one can integrate out the massive particles and thus obtain a one-loop effective action for the gauge fields. In the regime where charge-independent contributions to higher-derivative terms in the action are sufficiently small, it is then possible to derive constraints on the charge-to-mass ratios of the massive particles from requiring that photons propagate causally and have an analytic S-matrix. We thus find that the theories need to contain bifundamentals and satisfy a version of the weak gravity conjecture known as the convex-hull condition. Demanding self-consistency of the constraints under Kaluza-Klein compactification, we furthermore show that, for scalars, they imply a stronger version of the weak gravity conjecture in which the charge-to-mass ratios of an infinite tower of particles are bounded from below. We find that the tower must again include bifundamentals but does not necessarily have to occupy a charge (sub-)lattice.

The axionic weak gravity conjecture predicts the existence of instantons whose actions are less than their charges in appropriate units. We show that the conjecture is satisfied for the axion-dilaton-gravity system if we assume duality constraints on the higher derivative corrections in addition to positivity bounds which follow from unitarity, analyticity, and locality of UV scattering amplitudes. On the other hand, the conjecture does not follow if we assume the positivity bounds only. This presents an example where derivation of the weak gravity conjecture requires more detailed UV information than the consistency of scattering amplitudes.