The Weak Gravity Conjecture and Effective Field Theory

Abstract: The Weak Gravity Conjecture (WGC) is a proposed constraint on theories with gauge fields and gravity, requiring the existence of light charged particles and/or imposing an upper bound on the field theory cutoff $\Lambda$. If taken as a consistency requirement for effective field theories (EFTs), it rules out possibilities for model-building including some models of inflation. I demonstrate simple models which satisfy all forms of the WGC, but which through Higgsing of the original gauge fields produce low-energy EFTs with gauge forces that badly violate the WGC. These models illustrate specific loopholes in arguments that motivate the WGC from a bottom-up perspective; for example the arguments based on magnetic monopoles are evaded when the magnetic confinement that occurs in a Higgs phase is accounted for. This indicates that the WGC should not be taken as a veto on EFTs, even if it turns out to be a robust property of UV quantum gravity theories. However, if the latter is true then parametric violation of the WGC at low energy comes at the cost of non-minimal field content in the UV. I propose that only a very weak constraint is applicable to EFTs, $\Lambda \lesssim \left(-\log g \right)^{-1/2} M_\text{pl}$ where $g$ is the gauge coupling, motivated by entropy bounds. Remarkably, EFTs produced by Higgsing a theory that satisfies the WGC can saturate but not violate this bound.