# Repulsive Forces and the Weak Gravity Conjecture

## TL;DR

This paper examines two formulations of the Weak Gravity Conjecture involving massless scalar fields, analyzing their evidence, implications, and the possibility of a unified stronger criterion.

## Contribution

It clarifies the precise formulations of the two main versions of the Weak Gravity Conjecture and explores the evidence and implications for black holes and strong conjecture forms.

## Key findings

- Both conjectures are likely true based on current evidence.
- Implications for black hole physics are discussed.
- A potential stronger criterion unifying both conjectures is proposed.

## Abstract

The Weak Gravity Conjecture is a nontrivial conjecture about quantum gravity that makes sharp, falsifiable predictions which can be checked in a broad range of string theory examples. However, in the presence of massless scalar fields (moduli), there are (at least) two inequivalent forms of the conjecture, one based on charge-to-mass ratios and the other based on long-range forces. We discuss the precise formulations of these two conjectures and the evidence for them, as well as the implications for black holes and for "strong forms" of the conjectures. Based on the available evidence, it seems likely that both conjectures are true, suggesting that there is a stronger criterion which encompasses both. We discuss one possibility.