  In this note we show that models of natural inflation based on closed string
axions are incompatible with the weak gravity conjecture (WGC). Specifically,
we use T-duality in order to map the bounds on the charge-to-mass ratio of
particles imposed by the WGC, to constraints on the ratio between instanton
actions and axion decay constants. We use this connection to prove that if the
WGC holds, even when multiple axions are present and mix with each other, one
cannot have large axion decay constants while remaining in a regime of
perturbative control. We also discuss the extension of the WGC to discrete
symmetries and its possible impact on models with axion monodromy, and the
distinction between the strong and mild versions of the WGC. Finally, we offer
some speculations regarding the import of these results to the general theory
of inflation.
