# Infinite Distances and the Axion Weak Gravity Conjecture

## TL;DR

This paper provides evidence supporting the axion Weak Gravity Conjecture by analyzing infinite distance limits in Calabi-Yau compactifications, showing that instantons prevent violations of the conjecture.

## Contribution

It demonstrates that in all infinite distance limits, a tower of instantons ensures the multi-axion Weak Gravity Conjecture holds, generalizing recent Swampland Distance Conjecture insights.

## Key findings

- Instanton towers prevent convex hull violations in axion limits
- Results apply broadly using Hodge metric growth and sl(2)-splittings
- Supports the axion Weak Gravity Conjecture in string compactifications

## Abstract

The axion Weak Gravity Conjecture implies that when parametrically increasing the axion decay constants, instanton corrections become increasingly important. We provide strong evidence for the validity of this conjecture by studying the couplings of R-R axions arising in Calabi-Yau compactifications of Type IIA string theory. Specifically, we consider all possible infinite distance limits in complex structure moduli space and identify the axion decay constants that grow parametrically in a certain path-independent way. We then argue that for each of these limits a tower of D2-brane instantons with decreasing actions can be identified. These instantons ensure that the convex hull condition relevant for the multi-axion Weak Gravity Conjecture cannot be violated parametrically. To argue for the existence of such instantons we employ and generalize recent insights about the Swampland Distance Conjecture. Our results are general and not restricted to specific examples, since we use general results about the growth of the Hodge metric and the sl(2)-splittings of the three-form cohomology associated to each limit.