Ultraviolet-Infrared Bounds and Minimum Coupling in Effective Field Theories

TL;DR

This paper introduces a new, simpler argument for a lower bound on U(1) gauge couplings in effective field theories, based on quantum uncertainty, Lorentz invariance, and entropy bounds, refining previous bounds and exploring phenomenological implications.

Contribution

It presents a novel, straightforward derivation of the gauge coupling lower bound using fundamental principles and extends the Cohen-Kaplan-Nelson bound to include degrees of freedom.

Findings

Stronger lower bounds on U(1) couplings using CKN relation

Extension of CKN bound accounting for degrees of freedom

Discussion of phenomenological implications of the bounds

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.