Scalar Fields, Hierarchical UV/IR Mixing and The Weak Gravity Conjecture

TL;DR

This work investigates how the Weak Gravity Conjecture (WGC) generalizes in the presence of massless scalar fields and whether it can bind a particle’s mass $m$ well below the UV cut-off scale, signaling UV/IR mixing. By deriving a scalar-augmented bound ${\cal Q}^2 \geq m^2 + g^{ij}\partial_i m \partial_j m$ and examining a 5D-to-4D dimensional reduction, the authors show that $m$ can be constrained by an IR scale $\beta M_p$ with $\beta^2 = g^2 - \mu^2$, potentially much smaller than the UV scale $\Lambda_{UV} \sim g M_p$. They provide evidence that this mixing is tied to nonlocal effects (like the axion Wilson line) and discuss quantum corrections and naturalness, including SUSY-inspired protections and the challenges of maintaining a small $\beta$ under UV completions. The results offer a novel perspective on naturalness in quantum gravity, while highlighting that a full solution likely requires a mechanism that dynamically enforces the IR bound without hand-tuning. If robust, this UV/IR interplay could illuminate how high-energy gravity constrains low-energy scalar masses and couplings in ways observable via nonlocal gauge-scalar interactions.

Abstract

The Weak Gravity Conjecture (WGC) bounds the mass of a particle by its charge. It is expected that this bound can not be below the ultraviolet cut-off scale of the effective theory. Recently, an extension of the WGC was proposed in the presence of scalar fields. We show that this more general version can bound the mass of a particle to be arbitrarily far below the ultraviolet cut-off of the effective theory. It therefore manifests a form of hierarchical UV/IR mixing. This has possible implications for naturalness. We also present new evidence for the proposed contribution of scalar fields to the WGC by showing that it matches the results of dimensional reduction. In such a setup the UV/IR mixing is tied to the interaction between the WGC and non-local gauge operators.