Supersymmetric Gauge Theory and Superstring Geometry

超对称规范理论和超弦几何

基本信息

批准号：
10209201
负责人：
SATOH Yuji
金额：
$ 5.44万
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 on Priority Areas (B)
财政年份：
1998
资助国家：
日本
起止时间：
1998 至 2001
项目状态：
已结题

来源：
https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-10209201/
关键词：
supersymmetry string theory D-brane Calbi-Yau manifold Seiberg-Witten theory black hole AdS CFT correspondence non-commutative geometry Dブレインカイラルフェルミオン Ads D-brane 位相的場の理論

项目摘要

The purpose of this research was to study superstring theory and moduli spaces of supersymmetric gauge theories ('superstring geometry') by various mathematical and physical considerations. and verify the superstring duality in quantitative and rigorous manners.In 1998 (academic year), we derived the WDVV equations for some four-dimensional supersymmetric gauge theories, generalized related Donaldson-Witten invariants, and determined the Seiberg-Witten geometries in the cases with the gauge groups of the exceptional type. A rigorous description of the moduli spaces was also obtained by embedding them into M-theory.In 1999, we obtained the low-energy effective theories of the four-dimensional supersymmetric gauge theories with the exceptional-type flavor symmetries, and clarified its relation to five-dimensional theories. We also found a systematic method for analyzing D-branes on orbifold singularities of Calabi-Yau manifolds, and the generating function for the number of rational curv … More es in rational elliptic surfaces. Moreover, we systematically constructed the superconformal algebras in the AdS/CFT correspondence, which is related to the string duality.In 2000, we showed the dualities between some string junctions and the D-branes on del Pezzo surfaces in Calabi-Yau manifolds, and analyzed in detail the superconformal algebras related to the degenerated Calabi-Yau manifolds of the ADE type. We also obtained the exact correlation functions of the CFT with the AdS_3 target space and, using the AdS/CFT correspondence, clarified properties of the three-dimensional black hole and field theories on non-commutative geometries.In 2001, we found the prepotentials and Seiberg-Witten curves for the four-dimensional compactified models obtained from the six-dimensional non-critical string theory with the E_8 symmetry. We also derived rigorous properties about the operator product expansion for the AdS_3 CFT and the soliton scattering on non-commutative geometries.In this way, we obtained many useful and rigorous results about the superstring geometry and the string duality. Less

这项研究的目的是通过各种数学和物理考虑，研究超对称规格理论（“超串几何”）的超对称规定理论的模量空间。并验证定量和严格的举止的超音双重性。在1998年（学年），我们为某些四维超级对称理论的WDVV方程得出了WDVV方程，并确定了Seiberg-with的广义相关的Donaldson-Witten Infortiants，并确定了Seiberg-Withtenter-with Interications的情况。还通过将它们嵌入M理论来获得模量空间的严格描述。在1999年，我们获得了具有异常的型风味对称性的四维超级对称理论的低能量有效理论，并阐明了其与五维理论的关系。我们还发现了一种系统的方法，用于分析calabi-yau歧管的Orbifold奇异性上的D型晶体，以及用于理性曲线数量的生成函数…在有理椭圆形表面中更多的ES。 Moreover, we systematically constructed the superconformal algebras in the AdS/CFT correspondence, which is related to the string duality.In 2000, we showed the dualities between some string junctions and the D-branes on del Pezzo surfaces in Calabi-Yau manifolds, and analyzed in detail the superconformal algebras related to the degenerated Calabi-Yau manifolds of the ADE type.我们还获得了CFT与ADS_3目标空间的确切相关函数，并使用ADS/CFT对应关系，在2001年进行了三维黑洞和现场理论的澄清属性。我们还获得了有关ADS_3 CFT的操作产品扩展和非交通差异的孤子散射的严格属性。在这种方式上，我们获得了许多有关SuperString几何形状和字符串二元性的有用和严格的结果。较少的