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.
