Asymptotic limits of SCFTs and their relation to corresponding geometric structures, combining techniques from SCFT, noncommutative geometry, and algebraic geometry

SCFT 的渐近极限及其与相应几何结构的关系，结合 SCFT、非交换几何和代数几何的技术

• 批准号: 42963613
• 负责人: Professorin Dr. Katrin Wendland
• 金额: --
• 依托单位: School of Mathematics
• 依托单位国家: 德国
• 项目类别: Priority Programmes
• 财政年份: 2007
• 资助国家: 德国
• 起止时间: 2006-12-31 至 2008-12-31
• 项目状态: 已结题
• 来源: https://gepris.dfg.de/gepris/projekt/42963613?language=en
• 关键词: Asymptotic; limits; SCFTs; their; relation

The project aims to extend the previously developed notion of limiting processes for conformal field theories to the supersymmetric setting. It is expected that by means of techniques from noncommutative geometry in the resulting degenerate superconformal field theories, geometric interpretations can be obtained which include a metric, a dilaton, and a complex structure along with appropriate Dirac operators. The resulting degenerate geometries shall be compared and preferably identified with those Gromov-Hausdorff type limits that play a vital role in the context of mirror symmetry e.g. in the work of Siebert and collaborators, which is already funded under the umbrella of the SPP 1154. The project also includes applications to an important class of examples which is expected to yield interesting insights in singularity theory. Altogether a complete geometric understanding for the entire structure that arises in limits of SCFTs is aimed for.

该项目的目的是扩展以前开发的概念限制过程的共形场理论的超对称设置。预计通过非对易几何的技术，在由此产生的退化超共形场论，几何解释可以得到，其中包括一个度量，一个量子，和一个复杂的结构沿着适当的狄拉克运营商。将所得的简并几何形状与Gromov-Hausdorff类型极限进行比较，并最好与Gromov-Hausdorff类型极限进行识别，这些极限在镜像对称性的背景下发挥着至关重要的作用，例如在Siebert和合作者的工作中，该工作已经在SPP的保护下得到资助1154。该项目还包括应用一类重要的例子，预计将产生有趣的见解奇异理论。总之，一个完整的几何理解的整个结构中出现的限制SCFT的目的。