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

• Applicant: Professorin Dr. Katrin Wendland
• Subject Area: Mathematics
• Term: from 2007 to 2009
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 42963613

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.

• DFG Programme: Priority Programmes
• Subproject of: SPP 1154: Global Differential Geometry