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Four-dimensional Superconformal Field Theory and String Duality

四维超共形场论和弦对偶性

基本信息

批准号：
09640335
负责人：
YANG Sung-kil
金额：
$ 1.47万
依托单位：
University of Tsukuba
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (C)
财政年份：
1997
资助国家：
日本
起止时间：
1997 至 1999
项目状态：
已结题

项目摘要

1. Studying the low-energy effective action of four-dimensional N = 2 supersymmetric gauge theory in the Coulomb branch, we find an intimate relation between the Seiberg-Witten theory and the ADE simple singularity theory. Given spectral curves of the periodic Toda system as Seiberg-Witten curves, we calculate the instanton corrections in the low-energy effective potential. The result is in agreement with that obtained by the microscopic instanton calculus. Our results imply a deep relevance of two-dimensional topological gravity to four-dimensional Seiberg-Witten theory.2. Considering four-dimensional N = 1 supersymmetric gauge theory with the ADE gauge group coupled to adjoint matters, we derive the low-energy effective superpotential in the confining phase of U (1) photon. As a result, we obtain the complex curves for N = 2 gauge theories and propose the Seiberg-Witten geometry for N = 2 EィイD26ィエD2 gauge theory with massive fundamental hypermultiplets. The relevant manifold is described as a fibration of the ALE space of EィイD26ィエD2 type. Then we determine the Seiberg-Witten geometry for N = 2 SO and SU theory with massive spinor and vector matters by breaking the gauge symmetry of N = 2 EィイD26ィエD2 theory with massive fundamental matters.3. We study mass deformations of N = 2 superconformal theories with ADE global symmetries on a D3-brane in detail. As an extension of this work, elliptic curves for the IIB 7-brane configurations realizing the E-type affine Lie algebras are systematically derived from the cubic equation for a rational elliptic surface. Moreover, we analyze the structure of singularities, Mordell-Weil lattices and torsions of a rational elliptic surface using string junctions in the background of 12 IIB 7-branes, and find complete agreement with the classification of the Mordell-Weil lattices.

1.通过研究四维N = 2超对称规范理论在库仑分支中的低能有效作用量，发现Seiberg-Witten理论与ADE简单奇点理论有着密切的联系。给定周期户田系统的谱曲线为Seiberg-Witten曲线，计算了低能有效势下的瞬子修正。所得结果与微观瞬子计算结果一致。我们的结果暗示了二维拓扑引力与四维Seiberg-Witten理论的深刻关联.考虑四维N = 1超对称规范理论，在ADE规范群与伴随物质耦合的情况下，导出了U（1）光子束缚相的低能有效超势.结果得到了N = 2规范理论的复曲线，并提出了N = 2 E_（26）E_（26）D_（22）规范理论的Seiberg-Witten几何.相关的流形被描述为E D26 D2型ALE空间的纤维化。然后，通过破缺N = 2的E_（26）E_（26）E_（26）D_2理论的规范对称性，确定了N = 2的SO和SU理论的Seiberg-Witten几何.本文详细研究了D3-膜上具有ADE整体对称性的N = 2超共形理论的质量形变。作为这一工作的扩展，实现E-型仿射李代数的IIB 7-膜配置的椭圆曲线被系统地从有理椭圆曲面的三次方程导出。此外，我们分析了结构的奇点，Mordell-Weil格和挠的一个合理的椭圆表面使用弦结的背景下的12 IIB 7-膜，并找到完全符合的分类的Mordell-Weil格。