arXiv 2105.022322021-05hep-thmath.AG

一般渐近Calabi-Yau周期的建模

Modeling General Asymptotic Calabi-Yau Periods

Brice Bastian, Thomas W. Grimm, Damian van de Heisteeg

备注：: 63 pages, 6 figures, updated references, fixed typos, minor improvements of some periods

摘要：

为了揭示构成渐近Swampland拓扑基础的基本结构，我们开始了对Calabi- Yau流形的渐近周期向量的一般研究。我们的策略是利用所施加的约束的完整性，对称性和积极性，这是形式化的渐近霍奇理论。我们使用这些一般原则来研究复杂结构模空间中任何边界附近的周期，并解释了导致指数抑制校正的大多数边界附近必须存在一致性。唯一的例外是周期向量附近的研究充分的大型复杂结构点。连同可能的边界的分类，我们的程序使得有可能构建这些渐近周期的一般模型。这种构造的起点是分类边界的sl（2）-数据，我们使用它来构造称为幂零轨道的渐近霍奇分解。然后，我们使用后者来确定渐近周期向量。我们明确地进行这个程序的所有可能的一个和两个模量边界的卡-丘三倍，并写下一般模型的渐近周期。

英文摘要：

In the quests to uncovering the fundamental structures that underlie some of the asymptotic Swampland conjectures we initiate the general study of asymptotic period vectors of Calabi- Yau manifolds. Our strategy is to exploit the constraints imposed by completeness, symmetry, and positivity, which are formalized in asymptotic Hodge theory. We use these general principles to study the periods near any boundary in complex structure moduli space and explain that near most boundaries leading exponentially suppressed corrections must be present for consistency. The only exception are period vectors near the well-studied large complex structure point. Together with the classification of possible boundaries, our procedure makes it possible to construct general models for these asymptotic periods. The starting point for this construction is the sl(2)-data classifying the boundary, which we use to construct the asymptotic Hodge decomposition known as the nilpotent orbit. We then use the latter to determine the asymptotic period vector. We explicitly carry out this program for all possible one- and two-moduli boundaries in Calabi-Yau threefolds and write down general models for their asymptotic periods.

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摘要：

英文摘要：

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