Three-form periods on Calabi-Yau fourfolds: toric hypersurfaces and F-theory applications
Three-form periods on Calabi-Yau fourfolds: toric hypersurfaces and F-theory applications
复制标题
卡拉比-丘四重体上的三型周期：复曲面超曲面和 F 理论应用
DOI：
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发表时间：
2017
影响因子：
5.4
通讯作者：
Thomas W. Grimm
中科院分区：
文献类型：
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作者：
S. Greiner;Thomas W. Grimm
卡拉比-丘四重几何的研究与弦理论、M 理论和 F 理论向各个维度的紧致化有关。这项工作引入了数学机制来推导非平凡三形式的周期的完整模依赖性，四重形式在环面环境空间中实现为超曲面。它为确定这些形式的 Picard-Fuchs 型微分方程和积分表达式奠定了基础。关键工具是观察到，复曲面环境空间中四重超曲面上的非平凡三形式总是源于由在黎曼曲面上纤维化的复曲面树构建的约数。然后，三型周期与这些黎曼曲面的一型周期具有重要的相关性。一般来说，已知三型周期在复杂结构模空间上全纯变化，并且在四重紧化中产生的有效作用中发挥着重要作用。我们讨论了 F 理论紧化的两个明确的例子，其中三种形式的周期决定了轴子衰变常数。
The study of the geometry of Calabi-Yau fourfolds is relevant for compactifications of string theory, M-theory, and F-theory to various dimensions. This work introduces the mathematical machinery to derive the complete moduli dependence of the periods of non-trivial three-forms for fourfolds realized as hypersurfaces in toric ambient spaces. It sets the stage to determine Picard-Fuchs-type differential equations and integral expressions for these forms. The key tool is the observation that non-trivial three-forms on fourfold hypersurfaces in toric ambient spaces always stem from divisors that are build out of trees of toric surfaces fibered over Riemann surfaces. The three-form periods are then non-trivially related to the one-form periods of these Riemann surfaces. In general, the three-form periods are known to vary holomorphically over the complex structure moduli space and play an important role in the effective actions arising in fourfold compactifications. We discuss two explicit example fourfolds for F-theory compactifications in which the three-form periods determine axion decay constants.