On Axionic Field Ranges, Loopholes and the Weak Gravity Conjecture

TL;DR

The note analyzes how the Weak Gravity Conjecture constrains axion-based natural inflation, arguing that a strong form of the conjecture bounds the axion field range and challenges non-monodromic large-field models. It establishes a bound on the axion diameter, \mathcal{D}, via a convex-hull argument, showing that under perturbative control the maximal well-behaved range satisfies \mathcal{D} \le 2\pi. The authors scrutinize proposed loopholes that attempt to balance spectator (WGC-satisfying) instantons with dominant non-perturbative effects, highlighting substantial obstacles in UV completions, especially the need to separate spectator and dominant instantons and the difficulty of violating the strong-WGC. They further discuss gravitational and gauge instantons, higher-order instanton corrections, and kinetic alignment, arguing that achieving a parametrically large field range without conflicting with the WGC remains highly nontrivial. Overall, the results reinforce the view that axion-driven natural inflation is challenging within quantum gravity frameworks, and any viable loophole would require a concrete, consistent UV realization which, to date, lacks compelling evidence.

Abstract

In this short note we clarify some aspects of the impact that the Weak Gravity Conjecture has on models of (generalized) natural inflation. We address in particular certain technical and conceptual concerns recently raised regarding the stringent constraints and conclusions found in our previous work (arXiv:1503.04783). We also point out the difficulties faced by attempts to evade these constraints. These new considerations improve the understanding of the quantum gravity constraints we found and further support the conclusion that it remains challenging for axions to drive natural inflation.