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

TL;DR

This paper explores an extended Weak Gravity Conjecture involving scalar fields, revealing hierarchical UV/IR mixing and implications for naturalness, supported by evidence from dimensional reduction and gauge operator interactions.

Contribution

It demonstrates that the extended WGC with scalar fields allows the particle mass to be arbitrarily below the UV cutoff, revealing hierarchical UV/IR mixing and providing new evidence for scalar contributions.

Findings

Extended WGC bounds particle mass far below UV cutoff

Hierarchical UV/IR mixing observed in scalar field scenarios

Scalar contributions to WGC match dimensional reduction results

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.