Gromov-Witten invariants of stable maps with fields

TL;DR

This paper develops a new all-genus Gromov-Witten theory for stable maps with fields, connecting Landau-Ginzburg models with classical quintic invariants through cosection localization.

Contribution

It constructs the Gromov-Witten invariants of stable maps with fields for projective space, linking Landau-Ginzburg models to classical invariants via a novel algebro-geometric approach.

Findings

Invariants coincide with classical quintic Gromov-Witten invariants up to sign.

Introduces cosection localization to define invariants in Landau-Ginzburg setting.

Provides a unified framework for all genus Gromov-Witten invariants with fields.

Abstract

We construct the Gromov-Witten invariants of moduli of stable morphisms to $\Pf$ with fields. This is the all genus mathematical theory of the Guffin-Sharpe-Witten model, and is a modified twisted Gromov-Witten invariants of $\Pf$. These invariants are constructed using the cosection localization of Kiem-Li, an algebro-geometric analogue of Witten's perturbed equations in Landau-Ginzburg theory. We prove that these invariants coincide, up to sign, with the Gromov-Witten invariants of quintics.