Planckian Axions and the Weak Gravity Conjecture

Thomas C. Bachlechner; Cody Long; Liam McAllister

doi:10.1007/JHEP01(2016)091

paper

Planckian Axions and the Weak Gravity Conjecture

arXiv:1503.07853 · doi:10.1007/JHEP01(2016)091

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 $N ≫ 1$ axions, super-Planckian axion diameters $D$ 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 $f_{1}^{2} \leq ... \leq f_{N}^{2}$ 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 $D < M_{pl}$ nor $D < N M_{pl}$ . We then estimate the actions of instantons that fulfill the WGC. The leading instanton action is bounded from below by $S \geq S M_{pl} / f_{N}$ , with $S$ a fixed constant, but in the universal limit $S ≳ S N M_{pl} / f_{N}$ . 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.

20 pages, 2 figures

Planckian Axions and the Weak Gravity Conjecture

Abstract

References in corpus (6)

Cited by in corpus (102)