Ultraviolet-Infrared Bounds and Minimum Coupling in Effective Field Theories

Abstract

We provide a simple new argument for a lower bound on the coupling of a $U(1)$ gauge interaction in an effective field theory (EFT), originally obtained from the Weak Gravity Conjecture. Our argument employs basic principles of quantum mechanical energy-time uncertainty and Lorentz invariance, plus Bekenstein's entropy bound on the ultraviolet (UV) and infrared (IR) scales of an EFT. We show that using an alternative UV-IR relation based on the Cohen-Kaplan-Nelson (CKN) bound results in a stronger lower bound on the $U(1)$ coupling, consistent with the more stringent nature of the CKN relation. Applicability of our reasoning to other interactions is briefly discussed. We also slightly extend the CKN bound, by accounting for the effective degrees of freedom, and examine some of its phenomenological implications.