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 \( \mathcal{D} \) 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 f 21 ≤ ⋅ ⋅ ⋅ ≤ f 2 N 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 \( \mathcal{D} \) < M pl nor \( \mathcal{D} \) < \( \sqrt{N}{M}_{\mathrm{pl}} \). We then estimate the actions of instantons that fulfill the WGC. The leading instanton action is bounded from below by \( S\ge \mathcal{S}\;{M}_{\mathrm{pl}}/{f}_N \), with \( \mathcal{S} \) a fixed constant, but in the universal limit \( S\gtrsim \mathcal{S}\sqrt{N}\ {M}_{\mathrm{pl}}/{f}_N \). 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.
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Bachlechner, T.C., Long, C. & McAllister, L. Planckian axions and the Weak Gravity Conjecture. J. High Energ. Phys. 2016, 91 (2016). https://doi.org/10.1007/JHEP01(2016)091
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DOI: https://doi.org/10.1007/JHEP01(2016)091