Differential equations for periods and super string and susy gauge theories

周期微分方程以及超弦和 Susy 规范理论

• 批准号: 09440021
• 负责人: YAMADA Yasuhiko
• 金额: $ 4.22万
• 依托单位: KOBE UNIVERSITY
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (B)
• 财政年份: 1997
• 资助国家: 日本
• 起止时间: 1997 至 1998
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-09440021/
• 关键词: Super symmetry; Seiberg-Witten theory; Period integrals; String thory; Mirror symmetry; Integrability; Painleve equation; Topological field theory; Seiberg-Witten 理論; Painleve 方程式; Calabi-Yau多様体; プレポテンシャル; 可積分系; 特異点理論

In this project, each of the three investigators carried out his research independently with in close co-operation. Inspiring with each other, we can obtain successful results more than our initial aim.1. Y.Yamada studied the relation between the integrable structure in the two dimensional quantum gravity and singularity theories. He found deep connections between the KP equations, Drinfeld-Sokolov equations and Painleve equations, and obtained successful results on the theory of Painleve equations and their symmetries. This result is expected to be applied to other problems in mathematical physics.2. S.K.Yang investigated the Seiberg-Witten curves (or more general geometries) in N = 2 susy gauge theories in systematic way with explicit examples. He clarify the profound relation with the singularity theories and determine the geometrical structures for exceptional gauge groups.3. S.Hosono has continued the research on the mirror symmetry. He made important contribution for the evaluation of the Gromov-Witten invariants for elliptic- or K3-fibered Calabi-Yau manifolds. There is also some progress in counting the higher genus curves from theoretical and computing points of view.

在这个项目中，三位研究者各自独立并密切合作进行研究。互相激励，我们就能取得比最初目标更成功的成果。 1． Y.Yamada研究了二维量子引力中的可积结构与奇点理论之间的关系。他发现了KP方程、Drinfeld-Sokolov方程和Painleve方程之间的深层联系，并在Painleve方程及其对称性理论方面获得了成功的结果。该结果有望应用于数学物理的其他问题。 2． S.K.Yang 用明确的例子系统地研究了 N = 2 susy 规范理论中的 Seiberg-Witten 曲线（或更一般的几何形状）。他阐明了与奇点理论的深刻关系，并确定了异常规范群的几何结构。 3． S.Hosono继续对镜像对称性进行研究。他对椭圆或 K3 纤维 Calabi-Yau 流形的 Gromov-Witten 不变量的评估做出了重要贡献。从理论和计算的角度来看，计算更高的亏格曲线也取得了一些进展。

项目成果

Yasuhiko Yamada: "Determinant formulas for the generalized Painleve^^,equations of type A" Nagoya Math.J.(印刷中). (1999)

Yasuhiko Yamada：“广义疼痛水平^^的行列式，A 型方程”Nagoya Math.J（出版中）。

Yasuhiko Yamada: "Determinant formulas for the gener-alized Painleve equations of type A" Nagoya Math.J.(in press). (1999)

Yasuhiko Yamada：“A 型广义 Painleve 方程的行列式”Nagoya Math.J.（出版中）。

Hiroaki Kanno: "Donaldson-Witten Functions of Massless N=2 Supersymmetric QCD" Nucl.Phys.B535. 512-530 (1998)

Hiroaki Kanno：“无质量 N=2 超对称 QCD 的 Donaldson-Witten 函数”Nucl.Phys.B535。

Masatoshi Noumi: "Higher order Painleve^^, equations of type A^<(1)>_ι" Funkicialaj Ekvacioj. 41. 408-503 (1998)

Masatoshi Noumi：“高阶疼痛水平 ^^，A 型方程 ^<(1)>_ι” Funkicialaj Ekvacioj 41. 408-503 (1998)

Masatoshi Noumi: "Symmetries in the fourth Painleve equation and Okamoto polynomials" Nagoya Math.J.(印刷中). (1999)

Masatoshi Noumi：“第四个 painleve 方程和冈本多项式中的对称性”Nagoya Math.J（出版中）。