Sharpening the Weak Gravity Conjecture with Dimensional Reduction

TL;DR

This paper examines how the Weak Gravity Conjecture (WGC) behaves under dimensional reduction, proposing a stronger lattice version to ensure its robustness across compactifications and exploring its implications for axions and black holes.

Contribution

It introduces a lattice form of the WGC that remains valid under compactification and extends the conjecture's applicability to axions and black branes.

Findings

WGC bounds weaken in the infrared after compactification

A superextremal particle must exist for every charge in the lattice

Gravitational instantons suggest a WGC for axions

Abstract

We investigate the behavior of the Weak Gravity Conjecture (WGC) under toroidal compactification and RG flows, finding evidence that WGC bounds for single photons become weaker in the infrared. By contrast, we find that a photon satisfying the WGC will not necessarily satisfy it after toroidal compactification when black holes charged under the Kaluza-Klein photons are considered. Doing so either requires an infinite number of states of different charges to satisfy the WGC in the original theory or a restriction on allowed compactification radii. These subtleties suggest that if the Weak Gravity Conjecture is true, we must seek a stronger form of the conjecture that is robust under compactification. We propose a "Lattice Weak Gravity Conjecture" that meets this requirement: a superextremal particle should exist for every charge in the charge lattice. The perturbative heterotic string satisfies this conjecture. We also use compactification to explore the extent to which the WGC applies to axions. We argue that gravitational instanton solutions in theories of axions coupled to dilaton-like fields are analogous to extremal black holes, motivating a WGC for axions. This is further supported by a match between the instanton action and that of wrapped black branes in a higher-dimensional UV completion.