Planckian Axions and the Weak Gravity Conjecture

TL;DR

This paper argues that in theories with many axions, the Weak Gravity Conjecture does not necessarily prevent super-Planckian axion field ranges, challenging previous claims and clarifying the relationship between axion decay constants and field diameters.

Contribution

It clarifies the relationship between the kinetic matrix and axion field range, and estimates instanton actions showing super-Planckian ranges are not excluded by the WGC.

Findings

Super-Planckian axion diameters are compatible with the WGC in theories with many axions.

The diameter of the axion fundamental domain depends on eigenvector orientations, not just eigenvalues.

Instanton actions are bounded from below, allowing large field ranges without unsuppressed potential contributions.

Abstract

Several recent works have claimed that the Weak Gravity Conjecture (WGC) excludes super-Planckian displacements of axion fields, and hence large-field axion inflation, in the absence of monodromy. We argue that in theories with $N\gg1$ axions, super-Planckian axion diameters $\cal{D}$ are readily allowed by the WGC. We clarify the nontrivial relationship between the kinetic matrix $K$ --- unambiguously defined by its form in a Minkowski-reduced basis --- and the diameter of the axion fundamental domain, emphasizing that in general the diameter is not solely determined by the eigenvalues $f_1^2 \le ... \le f_N^2$ of $K$: the orientations of the eigenvectors with respect to the identifications imposed by instantons must be incorporated. In particular, even if one were to impose the condition $f_N<M_{pl}$, this would imply neither ${\cal D}<M_{pl}$ nor ${\cal D}<\sqrt{N}M_{pl}$. We then estimate the actions of instantons that fulfill the WGC. The leading instanton action is bounded from below by $S \ge {\cal S} M_{pl}/f_N$, with ${\cal S}$ a fixed constant, but in the universal limit $S\gtrsim {\cal S} \sqrt{N}M_{pl}/f_N$. Thus, having $f_N>M_{pl}$ does not immediately imply the existence of unsuppressed higher harmonic contributions to the potential. Finally, we argue that in effective axion-gravity theories, the zero-form version of the WGC can be satisfied by gravitational instantons that make negligible contributions to the potential.