arXiv 2407.025652024-07-02hep-th

Orientifold Calabi-Yau 三流形：除子交换与多重反射

Orientifold Calabi-Yau Threefolds: Divisor Exchanges and Multi-Reflections

Xu Cao, Hongfei Gao, Xin Gao

备注：: 55 pages, 2 figures

AI总结：

该研究基于 Kreuzer-Skarke 数据库，利用含除子交换与多除子反射的 Z_2 对合构建逾3.2亿个 orientifold Calabi-Yau 三流形，并提出算法判定固定轨迹、O-plane 类型及 orbifold 极限性质。

摘要：

利用包含四维自反多面体的 Kreuzer-Skarke 数据库，我们系统地构建了一个新的 orientifold Calabi-Yau 三流形数据库，其条件为 h^{1,1}(X) ≤ 12。我们的方法涉及非平凡的 Z_2 对合，并结合了作用于这些 Calabi-Yau 三流形上的除子交换和多除子反射。每个真对合都会产生一个 orientifold Calabi-Yau 三流形，而我们构建了 320,386,067 个此类例子。我们开发了一种新算法，可显著降低确定这些对合下所有固定轨迹的复杂度，并阐明 O-plane 的类型。结果表明，在真对合下，大多数情形最终形成 O3/O7-plane 系统，而且其中多数还允许朴素的 Type IIB 弦真空。此外，我们确定了一种新的自由作用类型。我们还计算了这些 orientifold Calabi-Yau 三流形在 Z_2-orbifold 极限下的光滑性以及 Hodge 数的分裂。

英文摘要：

Using the Kreuzer-Skarke database of 4-dimensional reflexive polytopes, we systematically constructed a new database of orientifold Calabi-Yau threefolds with $h^{1,1}(X) \leq 12$. Our approach involved non-trivial $\mathbb{Z}_2$ involutions, incorporating both divisor exchanges and multi-divisor reflections acting on the Calabi-Yau threefolds. Each proper involution results in an orientifold Calabi-Yau threefolds and we constructed 320,386,067 such examples. We developed a novel algorithm that significantly reduces the complexity of determining all the fixed loci under the involutions, and clarifies the types of O-planes. Our results show that under proper involutions, the majority of cases end up with O3/O7-plane systems, and most of these further admit a naive Type IIB string vacua. Additionally, a new type of free action was determined. We also computed the smoothness and the splitting of Hodge numbers in the $\mathbb{Z}_2$-orbifold limit for these orientifold Calabi-Yau threefolds.

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