发表机构
Moscow Institute of Physics and Technology; Landau Institute for Theoretical Physics（莫斯科物理技术学院; 朗道理论物理研究所）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出构造BHK型Calabi-Yau轨形及其镜像对的算法，枚举216个环型多项式，发现两个构型具有三代夸克和轻子，对粒子物理模型构建有重要意义。
AI 中文摘要
本文提出并应用了一种算法，用于构造满足Berglund-Hubsch-Krawitz (BHK)型Calabi-Yau流形的轨形及其环型多项式的镜像对。对满足Calabi-Yau条件的环型多项式进行了完整枚举，得到216个唯一多项式。对每个多项式计算了欧拉示性数、代数和单态数目，并使用Roan的广义组合构造分析了扭曲扇区态。研究表明，所有研究的构型均不存在Roan对，表明在解决轨形奇点后，扭曲扇区对Hodge数差异的贡献为零。本工作的主要物理结果是发现了两个具有对角指数$\{74, 3, 3, 5, 3\}$和$\{74, 3, 5, 3, 3\}$的构型，其夸克和轻子代数为精确的三代（$N_{\ ext{gen}} = 3$），这对于构建现象学上现实的粒子物理模型具有关键意义。
英文摘要
In this paper, an algorithm for constructing orbifolds of Calabi-Yau manifolds of the Berglund-Hubsch-Krawitz (BHK) type and their mirror pairs for loop-type polynomials is proposed and applied. A complete enumeration of loop polynomials satisfying the Calabi-Yau condition was carried out, yielding 216 unique polynomials. For each polynomial, the Euler characteristics, the numbers of generations and singlets were computed, and the twisted sector states were analyzed using Roan's generalized combinatorial construction. It was established that Roan pairs are absent for all studied configurations, indicating a zero contribution of the twisted sectors to the difference in Hodge numbers upon resolving the orbifold singularities. The primary physical result of this work is the discovery of two configurations with diagonal exponents $\{74, 3, 3, 5, 3\}$ and $\{74, 3, 5, 3, 3\}$, for which the number of quark and lepton generations is precisely three ($N_{\text{gen}} = 3$), which is of key interest for constructing phenomenologically realistic models of particle physics.
Comments16 pages, 2 tables
