Planckian Axions and the Weak Gravity Conjecture

Understand

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.