Planckian axions and the Weak Gravity Conjecture

Abstract

Abstract: Several recent works [1-3] 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 ≫ 1 axions, super-Planckian axion diameters (Formula presented.) are readily allowed by the WGC. We clarify the non-trivial 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 f12 ≤ ⋅ ⋅ ⋅ ≤ fN2 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 fN< Mpl, this would imply neither (Formula presented.) < Mpl nor (Formula presented.) < (Formula presented.). We then estimate the actions of instantons that fulfill the WGC. The leading instanton action is bounded from below by (Formula presented.) , with (Formula presented.) a fixed constant, but in the universal limit (Formula presented.). Thus, having fN> Mpl 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.