Transplanckian axions !?
  We discuss quantum gravitational effects in Einstein theory coupled to
periodic axion scalars to analyze the viability of several proposals to achieve
superplanckian axion periods (aka decay constants) and their possible
application to large field inflation models. The effects we study correspond to
the nucleation of euclidean gravitational instantons charged under the axion,
and our results are essentially compatible with (but independent of) the Weak
Gravity Conjecture, as follows: Single axion theories with superplanckian
periods contain gravitational instantons inducing sizable higher harmonics in
the axion potential, which spoil superplanckian inflaton field range. A similar
result holds for multi-axion models with lattice alignment (like the
Kim-Nilles-Peloso model). Finally, theories with $N$ axions can still achieve a
moderately superplanckian periodicity (by a $\sqrt{N}$ factor) with no higher
harmonics in the axion potential. The Weak Gravity Conjecture fails to hold in
this case due to the absence of some instantons, which are forbidden by a
discrete $\mathbf{Z}_N$ gauge symmetry. Finally we discuss the realization of
these instantons as euclidean D-branes in string compactifications.
