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

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。预计通过所得简并超共形场论中的非对易几何技术，可以获得几何解释，其中包括度规、膨胀子和复杂结构以及适当的狄拉克算子，沿着。由此产生的简并几何形状应进行比较，并优选地与在镜像对称的背景下发挥重要作用的Gromov-Hausdorff类型限制进行识别，例如在Siebert和合作者的工作中，该工作已经在SPP 1154的保护伞下获得资助。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。

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.