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 h1,1 ≤ 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.
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Acknowledgments
We thank Manki Kim, Nate MacFadden, Jake McNamara, Richard Nally, Andres Rios-Tascon, Andreas Schachner, and Mike Stillman for helpful discussions. N.G., L.M., and J.M. were supported in part by NSF grant PHY-1719877. B.H. was supported by NSF grants PHY-1914934 and PHY-2112800. T.R. was supported in part by the Berkeley Center for Theoretical Physics; by the Department of Energy, Office of Science, Office of High Energy Physics under QuantISED Award DE-SC0019380 and under contract DE-AC02-05CH11231; and by the National Science Foundation under Award Number 2112880.
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Gendler, N., Heidenreich, B., McAllister, L. et al. Moduli space reconstruction and Weak Gravity. J. High Energ. Phys. 2023, 134 (2023). https://doi.org/10.1007/JHEP12(2023)134
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DOI: https://doi.org/10.1007/JHEP12(2023)134