Moduli spaces and symmetries in string theory

弦理论中的模空间和对称性

基本信息

批准号：
12640022
负责人：
SHIMIZU Yuji
金额：
$ 1.86万
依托单位：
International Christian University
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (C)
财政年份：
2000
资助国家：
日本
起止时间：
2000 至 2002
项目状态：
已结题

来源：
https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-12640022/
关键词：
raional elliptic surfaces Seiberg-Witten theory period map integrable system conformal field theory elliptic K3 surfaces drived category

项目摘要

On the theme of Seiberg-Witten theory approached through elliptic surfaces, Shimizu did the joint research with A.Tsuchiya (Nagoya Univ.), A.Kato (Unlv. Tokyo) Y.Saito (Univ. Tokyo), H.Awata (Univ. Tokyo) etc. Among others, we constructed the moduli space of marked rational elliptic surfaces and their period map, studied the inversion problem, the relation with simply elliptic singularities, constructed the elliptic Lie algebra and the elliptic Weyl group, and carried out the realization of a Seiberg-Witten integrable system. In 2002, we introduced the periods of elliptic K3 surfaces, the moduli and the derived category of coherent sheaves in order to enlarge our study and to look for the quantum analog of classical periodsUeno and Shimizu studied the degeneration behavior of the conformal blocks of the CFT with abelian currents as symmetries, and published a book on moduli theory. Ueno constructed a modular functor using CFT. From the viewpoint of deformation theory of complex structure, Saito reconsidered the space of initial values of the Painleve equations, introduced the notion of Okamoto-Painleve pairs, classified them and rewrited the differential equationsSuzuki studied weakly distance-regular digraphs and type II matrices associated with link invariants. Morimoto expressed the analytic functionals on the sphere as initial values of the heat functions. Yamakawa studied codimension one locally free action of solvable Lie groups

关于Seiberg-Witten理论的主题，Shimizu与A.Tsuchiya（Nagoya Univ。）进行了联合研究。实现Seiberg-Witten可集成系统。在2002年，我们介绍了椭圆形K3表面，模量和衍生类别的相干滑轮类别的时期，以扩大我们的研究，并寻找经典时期的量子类似物，并研究了Shimizu的量子类似物，研究了CFT的cft层的变性行为以阿贝里亚电流为对称性，并发表了一本关于模量理论的书。 Ueno使用CFT构建了模块化函子。从复杂结构的变形理论的角度来看，Saito重新考虑了Painleve方程的初始值的空间，引入了Okamoto-Painleve对的概念，对它们进行了分类，并重写了研究的微分方程，研究了与弱距离的距离指法和II类型II相关的II型矩阵链接不变。 Morimoto作为热函数的初始值表达了球体上的分析功能。 Yamakawa研究了Codimension的一个本地可解决的谎言组的动作