Abstract
We study infinite-distance limits in the complex structure moduli space of elliptic Calabi-Yau threefolds. In F-theory compactifications to six dimensions, such limits include infinite-distance trajectories in the non-perturbative open string moduli space. The limits are described as degenerations of elliptic threefolds whose central elements exhibit non-minimal elliptic fibers, in the Kodaira sense, over curves on the base. We show how these non-crepant singularities can be removed by a systematic sequence of blow-ups of the base, leading to a union of log Calabi-Yau spaces glued together along their boundaries. We identify criteria for the blow-ups to give rise to open chains or more complicated trees of components and analyse the blow-up geometry. While our results are general and applicable to all non-minimal degenerations of Calabi-Yau threefolds in codimension one, we exemplify them in particular for elliptic threefolds over Hirzebruch surface base spaces. We also explain how to extract the gauge algebra for F-theory probing such reducible asymptotic geometries. This analysis is the basis for a detailed F-theory interpretation of the associated infinite-distance limits that will be provided in a companion paper [1].
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Acknowledgments
We thank Hans-Christian von Bothmer, Vicente Cortes, Antonella Grassi, Martijn Kool and Helge Ruddat for useful discussions. R. A.-G. and T. W. are supported in part by Deutsche Forschungsgemeinschaft under Germany’s Excellence Strategy EXC 2121 Quantum Universe 390833306 and by Deutsche Forschungsgemeinschaft through a German-Israeli Project Cooperation (DIP) grant “Holography and the Swampland”. The work of S.-J. L. is supported by IBS under the project code IBS-R018-D1.
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Álvarez-García, R., Lee, SJ. & Weigand, T. Non-minimal elliptic threefolds at infinite distance. Part I. Log Calabi-Yau resolutions. J. High Energ. Phys. 2024, 240 (2024). https://doi.org/10.1007/JHEP08(2024)240
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DOI: https://doi.org/10.1007/JHEP08(2024)240