可定向复三维卡拉比-丘流形的计算与数据库构建  

Computation and database construction of orientifold Calabi-Yau threefolds

作　　者：高鸿飞 高昕 GAO Hong-Fei;GAO Xin(College of Physics,Sichuan University,Chengdu 610064,China)

机构地区：[1]四川大学物理学院,成都610064

出　　处：《四川大学学报(自然科学版)》2025年第2期465-471,共7页Journal of Sichuan University(Natural Science Edition)

基　　金：国家自然科学基金(12375065)。

摘　　要：为了满足IIB型弦理论紧致化的需求,我们基于Kreuzer和Skarke构建的多面体数据库,计算并生成了一个可定向复三维卡拉比-丘流形数据库.计算流程如下:首先,通过四维自反多面体构建一个四维Toric底空间,并确定该底空间中存在的一般复三维卡拉比-丘流形的超平面表达式.同时,通过分析除子的拓扑性质,确定底空间中可能存在的除子交换Z2对称性.进一步,我们计算了具有除子交换Z2对称性的复三维卡拉比-丘流形及其固定点等性质,并评估了其在IIB型弦理论紧致化中的适用性.在固定点计算过程中,我们对相关计算步骤进行了简化处理.统计结果表明,这种简化对固定点计算结果的影响小于1%,但显著减少了计算时间,从而大幅提高了计算效率.我们的研究不仅为IIB型弦理论紧致化提供了重要的数据支持,也展示了计算方法优化在复杂几何计算中的潜力.To address the requirements of compactification of type IIB string theory,we computed and generated a database of orientifold Calabi-Yau threefolds based on the polytope database constructed by Kreuzer and Skarke.The computational process proceeds as follows:First,a four-dimensional toric base space is constructed using four-dimensional reflexive polytopes,and the hypersurface expressions of general Calabi-Yau threefolds within this base space are determined.Simultaneously,by analyzing the topological properties of divisors,we identify possible divisor exchange symmetries within the base space.Furthermore,we computed Calabi-Yau threefolds with divisor exchange symmetries,calculated their fixed points and other properties,and evaluated their suitability for compactification in type IIB string theory.During the fixed point calculation process,we simplified certain computational steps.Statistical results indicate that this simplification im‑pacts the fixed point calculation by less than 1%,while significantly reducing computation time,thereby greatly enhancing efficiency.Our research not only provides important data support for type IIB string theory compactification but also demonstrates the potential of computational method optimization in complex geometric calculations.

关 键 词：卡拉比-丘流形 弦紧致化 IIB型弦理论 

分 类 号：O412.2[理学—理论物理]