Gromov–Witten Invariants of Stable Maps with Fields

We construct the Gromov–Witten invariants of moduli of stable maps to $\mathbb P^4$ with fields. This is the all genus mathematical theory of the Guffin–Sharpe–Witten model, and is a modified twisted Gromov–Witten invariant of $\mathbb P^4$. These invariants are constructed using the cosection localization of Kiem–Li, an algebro-geometric analog 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.