Enumerative Geometry of Calabi-Yau Manifolds and String Theory

卡拉比-丘流形的枚举几何与弦理论

• 批准号: 16540024
• 负责人: KAWAI Toshiya
• 金额: $ 2.05万
• 依托单位: Kyoto University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 2004
• 资助国家: 日本
• 起止时间: 2004 至 2006
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/en/grant/KAKENHI-PROJECT-16540024/
• 关键词: Calabi-Yau manifolds; string theory; Boicherds products; Gromov-witten invariants; 弦双対性; 楕円コホモロジー; ヤコビ形式; F理論; 混成弦

We investigated analogs of Borcherds products for Calabi-Yau threefolds. From a geometrical viewpoint, such products should count sheaves or D-branes on the manifolds. It is also expected that they are related to the Gromov-Witten potentials through certain asymptotic expansions. In the context of string theory they should count BPS states in type IIA string theory compactified on the Calabi-Yau manifolds. In this research we tried to develop a systematic method to construct such products or partial products when the Calabi-Yaus are elliptically fibered or K3 fibered. To certain extent, we have succeeded in this mission and obtained concrete expressions. Some consistency checks have been made and functional properties are being investigated. I am currently preparing the manuscript reporting these results.As a related subject we have studied the properties of vortices on nodal and cuspidal curves.

我们研究了borcherds产品的类似物，用于卡拉比野三倍。从几何观点来看，此类产品应在流形上计算带束或d-branes。还可以预期，通过某些渐近扩张，它们与格罗莫夫（Gromov）的潜力有关。在字符串理论的背景下，他们应该在calabi-yau歧管上压实的IIA型字符串理论中对BPS状态进行计数。在这项研究中，我们试图开发一种系统的方法来构建此类产品或部分产品时，当卡拉比（Calabi-Yaus）呈椭圆形纤维或K3纤维纤维时。在某种程度上，我们在这项任务中取得了成功，并获得了具体表达。已经进行了一些一致性检查，并正在研究功能属性。我目前正在准备报告这些结果的手稿。作为相关的主题，我们研究了涡旋在节点和尖曲线上的特性。

项目成果

Vortex and String

涡流和弦

• 发表时间: 2004
• 期刊: Publ.Res.lnst.Math.Sci.Kyoto 40
• 作者: Shiro Goto;Ken-ichi Yoshida;Toshiya Kawai
• 通讯作者: Toshiya Kawai

String and Vortex

弦与涡

• 发表时间: 2004
• 期刊: Publ.Res.Inst.Math.Sci.Kyoto 40
• 作者: Shiro Goto;Ken-ichi Yoshida;Toshiya Kawai;Toshiya Kawai
• 通讯作者: Toshiya Kawai