Axion decay constants away from the lamppost

TL;DR

This paper investigates the maximum possible axion field ranges in string theory compactifications, finding they are generally close to the Planck scale and related to geometric properties of Calabi-Yau manifolds.

Contribution

It introduces a method to determine axion decay constants in strongly coupled regions of moduli space using extended supersymmetry and Calabi-Yau geometry analysis.

Findings

Maximum axion decay constant is approximately 3.25 times the Planck mass.

Axion field ranges are linked to intersection and instanton numbers of Calabi-Yau geometries.

Field ranges are close to the reduced Planck mass in studied examples.

Abstract

It is unknown whether a bound on axion field ranges exists within quantum gravity. We study axion field ranges using extended supersymmetry, in particular allowing an analysis within strongly coupled regions of moduli space. We apply this strategy to Calabi-Yau compactifications with one and two K\"ahler moduli. We relate the maximally allowable decay constant to geometric properties of the underlying Calabi-Yau geometry. In all examples we find a maximal field range close to the reduced Planck mass (with the largest field range being 3.25 $M_P$). On this perspective, field ranges relate to the intersection and instanton numbers of the underlying Calabi-Yau geometry.