Weak Gravity Conjecture From Low Energy Observers' Perspective

Abstract: The Weak Gravity Conjecture (WGC) was proposed to constrain Effective Field Theories (EFTs) with Abelian gauge symmetry coupled to gravity. In this article, I study the WGC from low energy observers' perspective, and revisit the issue of to what extent the WGC actually constrains EFTs. For this purpose, for a given EFT, I introduce associated idealized low energy observers who only have access to the energy scale below the UV cut-off scale of the EFT. In the framework of EFT, there is a clear difference between the particles lighter than the UV cut-off scale and the particles which are heavier than the UV cut-off scale, as the lighter particles can be created below the UV cut-off scale while the heavier particles are not. This difference implies that the knowledge of the low energy observers on the stable heavy particles can be limited, as the availability of the stable heavy particles is determined by the environment prepared by some UV theory unknown to the low energy observers. The limitation of the knowledge of the low energy observers regarding the stable heavy particles whose mass is above the UV cut-off scale of the EFT leads to the limitation of the WGC for constraining EFTs. To illustrate these points in an example, I analyze a model proposed by Saraswat arXiv:1608.06951 which respects the WGC at high energy, but which may appear to violate the WGC for the low energy observers. Implications of the analysis to the bottom-up model buildings using EFTs are discussed.