Non-minimal Elliptic Threefolds at Infinite Distance I: Log Calabi-Yau Resolutions

with Seung-Joo Lee and Timo Weigand

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.

BibTex Citation

@article{Alvarez-Garcia:2023gdd,
    author = "\'Alvarez-Garc\'\i{}a, Rafael and Lee, Seung-Joo and Weigand, Timo",
    title = "{Non-minimal Elliptic Threefolds at Infinite Distance I: Log Calabi-Yau Resolutions}",
    eprint = "2310.07761",
    archivePrefix = "arXiv",
    primaryClass = "hep-th",
    reportNumber = "CTPU-PTC-23-44, ZMP-HH/23-14",
    month = "10",
    year = "2023"
}