论文标题
完整交集的数值指标和Kreuzer-Skarke Calabi-yau歧管
Numerical Metrics for Complete Intersection and Kreuzer-Skarke Calabi-Yau Manifolds
论文作者
论文摘要
我们介绍了神经网络，以计算数值ricci-flat cy cy量，以在Kähler和复杂的结构模仿空间的任何时刻与Kreuzer-Skarke Calabi-yau歧管，并引入包装cymetric，以提供这些技术的计算实现。特别是，我们开发和计算实现了这些歧管上点采样的方法。对神经网络的培训受到自定义损失功能的约束。 Kähler类是通过添加损失的组件来固定的，该组件强制执行某些线束的斜率以与拓扑计算匹配。我们的方法应用于各种歧管，包括Quintic歧管，Bi-cubic歧管和具有PICARD第二的Kreuzer-Skarke歧管。我们表明，可以从由此产生的RICCI-FLAT指标可靠地计算体积和线条束斜率。我们还应用结果来计算Bi-Abic上特定线条束上的近似Hermitian-yang-mills连接。
We introduce neural networks to compute numerical Ricci-flat CY metrics for complete intersection and Kreuzer-Skarke Calabi-Yau manifolds at any point in Kähler and complex structure moduli space, and introduce the package cymetric which provides computation realizations of these techniques. In particular, we develop and computationally realize methods for point-sampling on these manifolds. The training for the neural networks is carried out subject to a custom loss function. The Kähler class is fixed by adding to the loss a component which enforces the slopes of certain line bundles to match with topological computations. Our methods are applied to various manifolds, including the quintic manifold, the bi-cubic manifold and a Kreuzer-Skarke manifold with Picard number two. We show that volumes and line bundle slopes can be reliably computed from the resulting Ricci-flat metrics. We also apply our results to compute an approximate Hermitian-Yang-Mills connection on a specific line bundle on the bi-cubic.
