Moduli Space Reconstruction and Weak Gravity

TL;DR

This paper develops a method to reconstruct the moduli space of Calabi-Yau threefolds using Gopakumar-Vafa invariants, enabling explicit tests of the Weak Gravity Conjecture across various geometric phases.

Contribution

It introduces a novel approach to identify all geometric phases of Calabi-Yau threefolds and tests the Weak Gravity Conjecture using BPS state counts from Gopakumar-Vafa invariants.

Findings

All examples satisfy the tower/sublattice WGC.

Examples also satisfy the stronger lattice WGC.

Method applies to favorable Calabi-Yau threefold hypersurfaces with h^{1,1} ≤ 4.

Abstract

We present a method to construct the extended K\"ahler 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 K\"ahler 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.