Ultraviolet-Infrared Bounds and Minimum Coupling in Effective Field Theories

Understand

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.