Duality and modular form in topological gauge theory

拓扑规范理论中的对偶性和模形式

• 批准号: 10640081
• 负责人: KANNO Hiroaki
• 金额: $ 1.79万
• 依托单位: Hiroshima University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 1998
• 资助国家: 日本
• 起止时间: 1998 至 1999
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-10640081/
• 关键词: Instanton; Topological gauge theory; Special holonomy group; Supersymmetric cycle; 超対称ゲージ理論; 位相的場の量子論; Seiberg-Witten 理論

From the viewpoint of non-perturbative dynamics of supersymmetric gauge theory and dualities of superstring theory we have investigated the geometry of instanton moduli space in higher dimensions and its relation to supersymmetric cycles, which are naturally introduced on the manifold of special holonomy.We first argued that supersyrnmetric cycles play a significant role in the problem of compactifying the instanton moduli space in higher dimensions. As an explicit example we constructed the octonionic instanton solutions on a non-compact eight-dimensional manifold with Spin (7) holonomy. However, our understanding of the geometry of its moduli space is still incomplete and it is an open problem to construct a new kind of topological invariants based on the octonionic instanton moduli space.Quite recently a substantial progress has been made in the five dimensional supersymmetric gauge theory compactified on a circle, which was the research subject in 1998. It seems possible to understand the space-time instanton in topological gauge theory from the world-sheet instanton of string theory in which the mirror symmetry gives a powerful tool.

本文从超对称规范理论的非微扰动力学和超弦理论的对偶性出发，研究了高维瞬子模空间的几何及其与超对称圈的关系，指出了超对称圈在高维瞬子模空间的紧化问题中的重要作用.作为一个显式例子，我们构造了一个非紧的八维流形上的自旋（7）holonomy的八子瞬子解。然而，我们对其模空间几何的理解仍然是不完全的，在八元数瞬子模空间的基础上构造一种新的拓扑不变量是一个悬而未决的问题。最近，1998年的研究课题--在圆上紧化的五维超对称规范理论取得了实质性的进展。从弦论的世界片瞬子中理解拓扑规范论中的时空瞬子似乎是可能的，在弦论中镜像对称提供了一个强有力的工具。

项目成果

H. Kanno and Y. Yasui: "Yang-Mills instantons on quaternionic line bundle of Spin(7) holonomy"J. Geom. Phys.. (to be published).

H. Kanno 和 Y. Yasui：“Spin(7) 完整性四元数线束上的 Yang-Mills 瞬时子”J.

H.Kanno: "Donaldson-Witten Function of Massless N=2 Supersymmetric QCD" Nuclear Physics B. 535. 512-530 (1998)

H.Kanno：“无质量 N=2 超对称 QCD 的 Donaldson-Witten 函数”核物理 B. 535. 512-530 (1998)

H.KANNO,et.al.: "Yang-Mills Instanton on Quaternionic:Line Bundle of Spin(7) Holonomy"Journal of Geometry and Physics. (発表予定). (2000)

H.KANNO 等人：“Yang-Mills Instanton on Quaternionic: Line Bundle of Spin(7) Holonomy”《几何与物理学杂志》（即将出版）。

H.KANNO et al.: "Yang-Mills Instanton on Luaterninic Kine Bundle of Spin(7) Holonomy"Jounal of Geometry and Physics. (発表決定). (2000)

H.KANNO 等人：“Yang-Mills Instanton on Luaterninic Kine Bundle of Spin(7) Holonomy”《几何与物理学杂志》（已决定出版）（2000 年）。

H.Kannno: "Picard-Fuchs Equations and Prepotential of Five Dimensional SUSY Gauge Theory Compactified on a Circle" Nuclear Physics. 530. 73-98 (1998)

H.Kannno：“Picard-Fuchs 方程和五维 SUSY 规范理论在圆上的压缩”核物理。