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

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 $d\le 4$ 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 ($d\le 4$) 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 ${\mathcal{L}}_{\text{eff}}$.

18 pages; more details on the geometry and finite action

References in corpus (6)

• On the Geometry of the String Landscape and the Swampland
• The Swampland: Introduction and Review
• The String Landscape and the Swampland
• Special Geometry and the Swampland
• Twistorial Topological Strings and a tt* Geometry for N=2 Theories in 4d
• On the Hodge Metric of the Universal Deformation Space of Calabi-Yau Threefolds

Cited by in corpus (7)

• Moduli Space Holography and the Finiteness of Flux Vacua
• Weak Gravity Bounds in Asymptotic String Compactifications
• Bulk Reconstruction in Moduli Space Holography
• Swampland geometry and the gauge couplings
• Deformed WZW Models and Hodge Theory -- Part I
• Hitchhiker's Guide to the Swampland: The Cosmologist's Handbook to the string-theoretical Swampland Programme
• Stability of BPS States and Weak Coupling Limits