20250516 Jesse Straat

The goal of this talk is to introduce the concept of mirror symmetry. Mirror symmetry is a relation between Calabi–Yau threefolds that allows one to identify type IIA string theory on one Calabi–Yau threefold with type IIB on the other (known as its mirror manifold). To a mathematician, this makes it possible to calculate Gromov–Witten invariants by considering type IIB correlators, which are typically much easier to compute. We start off by constructing the A-twisted and B-twisted nonlinear sigma model QFT, and discussing what exactly makes these models nice, by identifying their BRST cohomology with cohomology on spacetime. We introduce the definition of mirror symmetry and its geometric implications, explicitly constructing a mirror manifold of the famous quintic threefold. If time permits, we will promote the twisted nonlinear sigma model to the types IIA and IIB string theory and explicitly showcase the emergence of Gromov–Witten invariants in type IIA string theory.

This talk will be accessible for both physicists and mathematicians who are interested in the geometric construction of topological string theories and mirror symmetry. For the mathematicians, it will be beneficial, but not necessary, to have a conceptual understanding of quantum field theory.