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

TL;DR

This paper demonstrates that the Weil-Petersson geometry of Calabi-Yau moduli spaces for dimensions up to four can be interpreted as gravitational instantons, linking string theory compactifications to solutions of Einstein gravity with matter.

Contribution

It establishes a novel connection between Calabi-Yau moduli space geometry and gravitational instantons within the context of string theory and the swampland program.

Findings

Moduli space geometries are gravitational instantons.

Calabi-Yau moduli spaces describe instantons of Einstein gravity coupled to matter.

Provides a geometric interpretation relevant for string compactifications.

Abstract

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 $\mathscr{L}_\text{eff}$.