Gromov-Witten invariants and localization

Understand

We give a pedagogical review of the computation of Gromov-Witten invariants via localization in 2D gauged linear sigma models.

• We explain the relationship between the two-sphere partition function of the theory and the Kahler potential on the conformal manifold.
• We show how the Kahler potential can be assembled from classical, perturbative, and non-perturbative contributions, and explain how the non-perturbative contributions are related to the Gromov-Witten invariants of the corresponding Calabi-Yau manifold.
• We then explain how localization enables efficient calculation of the two-sphere partition function and, ultimately, the Gromov-Witten invariants themselves.