arXiv 2008.017302020-08-04hep-th

界定克罗伊策-斯卡克景观

Bounding the Kreuzer-Skarke Landscape

Mehmet Demirtas, Liam McAllister, Andres Rios-Tascon

备注：: 29 pages, 8 figures

摘要：

通过构造和计算自反多面体的三角剖分，研究了具有大Hodge数的Calabi-Yau三重性。通过计算相关的二级多面体中的点，我们证明了Kreuzer-Skarke列表中的多面体的精细的、规则的、星形三角剖分的数目由$\binom{14,111}{494} \approx 10^{928}$上界。利用Anclin关于格点多边形三角剖分的一个结果，得到了列表中每个多面体的每个2-面的三角剖分个数的一个界。用这种方法我们证明了由Kreuzer-Skarke列表产生的拓扑不等价的Calabi-Yau超曲面的个数是由$10^{428}$上有界的.我们介绍了有效的算法来构造代表性的集合的Calabi-Yau超曲面，包括极端情况下$h^{1,1}=491$，我们研究的拓扑和物理数据的分布。最后，我们证明了神经网络可以准确地预测这些数据，一旦三角编码的第二多面体。

英文摘要：

We study Calabi-Yau threefolds with large Hodge numbers by constructing and counting triangulations of reflexive polytopes. By counting points in the associated secondary polytopes, we show that the number of fine, regular, star triangulations of polytopes in the Kreuzer-Skarke list is bounded above by $\binom{14,111}{494} \approx 10^{928}$. Adapting a result of Anclin on triangulations of lattice polygons, we obtain a bound on the number of triangulations of each 2-face of each polytope in the list. In this way we prove that the number of topologically inequivalent Calabi-Yau hypersurfaces arising from the Kreuzer-Skarke list is bounded above by $10^{428}$. We introduce efficient algorithms for constructing representative ensembles of Calabi-Yau hypersurfaces, including the extremal case $h^{1,1}=491$, and we study the distributions of topological and physical data therein. Finally, we demonstrate that neural networks can accurately predict these data once the triangulation is encoded in terms of the secondary polytope.

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