  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.
