%0 Journal Article %T Gromov-Witten invariants of stable maps with fields %A Huai-liang Chang %A Jun Li %J Mathematics %D 2011 %I arXiv %X 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. %U http://arxiv.org/abs/1101.0914v1