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.

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 方面。作为一个明确的例子，我们在具有自旋（7）载体的非紧凑型八维歧管上构建了八元素激体溶液。但是，我们对其模量空间的几何形状的理解仍然不完整，这是一个开放的问题，基于Octonionionic Intsonton Moduli空间构建一种新型的拓扑不变性。最近，在五个维度的超级对称理论中取得了五个尺寸的超级理论在1998年的范围内，这是一个实用的仪表，在五个维度的超级对象中取得了实质性的进展，这是在1998年的实例上。镜子对称性提供了强大工具的弦理论。

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: "A Note on Higher Dimensional Instantons and Supersymmetric Cycles"Progress of Theoretical Physics Supplement. 135. 18-28 (1999)

H.KANNO：“关于高维瞬时子和超对称循环的注释”理论物理进展补充。

H.KANNO: "A Note on Higher Dimensional Instantons and Supersymmetic Cycles"Progress.of Theoretical Physics Supplement. 135. 18-28 (1999)

H.KANNO：“关于高维瞬时子和超对称循环的注释”理论物理增刊的进展。