论文标题
分类用于弦现象学的除数拓扑
Classifying divisor topologies for string phenomenology
论文作者
论文摘要
在本文中，我们介绍了有利的Calabi Yau（Cy）三倍的分层拓扑的分类，其$ 1 \ leq h^{1,1}（cy）\ leq 5 $由Kreuzer-skarke数据库的四维反射型产生。根据一些经验观察，我们猜测，所谓的坐标分隔线的拓扑可以分为两类：（i）。 $χ_ {_ h}（d）\ geq 1 $，由$ \ {h^{0,0,0} = 1，\，\，h^{1,0} = 0，\，\，\，h^{2,0} =χ_ {2,0} χ_ {_ H}（d）\} $和（ii）。 $χ_ {_ h}（d）\ leq 1 $，由$ \ {h^{0,0,0} = 1，\，\，h^{1,0} = 1 - χ_ {_ h H}（_ h h}（d），\，\，h^，h^{2,0} = 0， χ_ {_ H}（d）\} $，其中$χ_ {_ H}（d）$表示算术属，而$χ（d）$表示Divisor $ d $的欧拉特征。我们介绍了大约140000个坐标分配的杂物数，与所有Cy三倍相对应，$ 1 \ leq h^{1,1}（cy）\ leq 5 $，对应于总计近16000个不同的CY几何形状。随后，我们认为我们的猜想可以帮助``绕过''cohomcalg对计算杂货数的坐标数量的需求，因此对于研究Cy三倍的cy三倍的$ h^{1,1} $的cy三倍的cy三倍的分裂拓扑的需要非常有用。现象学模型构建，例如，估计$ d3 $ tadpole的t（在反射率下），这是构建明确的全球模型的主要成分，这是由于多种不同的原因/兴趣，例如通过抗$ d3 $ d3 $ brane and（flat）flux vacua搜索。
In this article we present a pheno-inspired classification for the divisor topologies of the favorable Calabi Yau (CY) threefolds with $1 \leq h^{1,1}(CY) \leq 5$ arising from the four-dimensional reflexive polytopes of the Kreuzer-Skarke database. Based on some empirical observations we conjecture that the topologies of the so-called coordinate divisors can be classified into two categories: (i). $χ_{_h}(D) \geq 1$ with Hodge numbers given by $\{h^{0,0} = 1, \, h^{1,0} = 0, \, h^{2,0} = χ_{_h}(D) -1, \, h^{1,1} = χ(D) - 2 χ_{_h}(D) \}$ and (ii). $χ_{_h}(D) \leq 1$ with Hodge numbers given by $\{h^{0,0} = 1, \, h^{1,0} = 1 - χ_{_h}(D), \, h^{2,0} = 0, \, h^{1,1} = χ(D) + 2 - 4 χ_{_h}(D)\}$, where $χ_{_h}(D)$ denotes the Arithmetic genus while $χ(D)$ denotes the Euler characteristic of the divisor $D$. We present the Hodge numbers of around 140000 coordinate divisors corresponding to all the CY threefolds with $1 \leq h^{1,1}(CY) \leq 5$ which corresponds to a total of nearly 16000 distinct CY geometries. Subsequently we argue that our conjecture can help in ``bypassing" the need of cohomCalg for computing Hodge numbers of coordinate divisors, and hence can be significantly useful for studying the divisor topologies of CY threefolds with higher $h^{1,1}$ for which cohomCalg gets too slow and sometimes even breaks as well. We also demonstrate how these scanning results can be directly used for phenomenological model building, e.g. in estimating the $D3$-brane tadpole charge (under reflection involutions) which is a central ingredient for constructing explicit global models due to several different reasons/interests such as the de-Sitter uplifting through anti-$D3$ brane and (flat) flux vacua searches.
