  Motivated by the swampland program, we show that the Weil-Petersson geometry
of the moduli space of a Calabi-Yau manifold of complex dimension $d\leq4$ is a
gravitational instanton (i.e. a finite-action solution of the Euclidean
equations of motion of gravity with matter). More precisely, the moduli
geometry of Calabi-Yau $d$-folds ($d\leq4$) describes instantons of (E)AdS
Einstein gravity coupled to a standard chiral model.
  From the point of view of the low-energy physics of string/M-theory
compactified on the Calabi-Yau $X$, the various fields propagating on its
moduli space are the couplings appearing in the effective Lagrangian
$\mathscr{L}_\text{eff}$.
