Quasimap theory and its applications to mirror symmetry

Abstract

We dealt with quasimap theory and its applications to mirror symmetry. Especially, we suggested the way how to make conjectural formula explicitly, which is so called ``wall crossing formula", by accounting for the relationship between Gromov-Witten theory and quasimap theory. Also, we explained the relationship between Landau-Ginzburg model and quasimap thoery for known cases. Using this result, we calculated the genus 1 Gromov-Witten invariants for some Calabi-Yau varieties. Finally, we showed that how A-twisted gauged linear sigma model and quasimap theory are related and some correlators defined separately in both theories are matched in some cases. The matched correlators are well-known quatity, so called Yukawa coupling.