Moduli spaces of Calabi-Yau d-folds as gravitational-chiral instantons

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 <= 4 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 <= 4) 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 .