Title of the project: Calabi-Yau Moduli Spaces and Special Regions therein
Name of the VDSP student: David Erkinger
Project supervised by: Johanna Knapp, Stefan Fredenhagen

I am a PhD student in the mathematical physics group. I am in the final year of my studies. My research is focused on moduli spaces of Calabi-Yau compactifications in string theory.

The concept of compactification describes the process of obtaining 4-dimensional physics from string theory, which requires 10 dimensions for consistency. Calabi-Yau (CY) spaces are a possible type of compactification spaces. These Calabi-Yaus come with parameters, called moduli, which parametrise the size and the shape of the compactification space. I study these moduli spaces with the help of a gauge theory, called gauged linear sigma model (GLSM). Coupling constants in this model can be identified with coordinates on the moduli space. Throughout the moduli space we encounter different models describing the low energy (IR) physics. The GLSM provides a unifying high energy (UV) description of these models. This is depicted in the image. Typical models one encounters are Non-linear sigma models (NLSM), hybrid models (HYB) and Landau-Ginzburg models (LG). A better understanding of these moduli spaces and the various models therein could provide insights to the swampland program of string theory and the mathematical discipline of enumerative geometry.

Fredenhagen group