Moduli Space Reconstruction and Weak Gravity

Abstract

We present a method to construct the extended Kähler cone of any Calabi-Yau threefold by using Gopakumar-Vafa invariants to identify all geometric phases that are related by flops or Weyl reflections. In this way we obtain the Kähler moduli spaces of all favorable Calabi-Yau threefold hypersurfaces with $h^{1,1}\le 4$, including toric and non-toric phases. In this setting we perform an explicit test of the Weak Gravity Conjecture by using the Gopakumar-Vafa invariants to count BPS states. All of our examples satisfy the tower/sublattice WGC, and in fact they even satisfy the stronger lattice WGC.

arXiv comment29 pages + appendices, 8 illustrations; v2: matches published version

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• An Introduction to the Weak Gravity Conjecture
• Hitchhiker's Guide to the Swampland: The Cosmologist's Handbook to the string-theoretical Swampland Programme