Gromov-Witten invariants and localization

TL;DR

This paper reviews how localization techniques in 2D gauged linear sigma models facilitate the computation of Gromov-Witten invariants, linking physical partition functions to geometric invariants of Calabi-Yau manifolds.

Contribution

It provides a pedagogical overview of calculating Gromov-Witten invariants using localization, connecting two-sphere partition functions with Kahler potentials and non-perturbative effects.

Findings

Localization enables efficient Gromov-Witten invariant calculations

Partition functions relate to Kahler potentials on conformal manifolds

Non-perturbative contributions encode geometric invariants

Abstract

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.