Polynomial structure of Gromov–Witten potential of quintic $3$-folds


We prove two structure theorems for the Gromov-Witten theory of the quintic threefolds, which together give an effective algorithm for the all genus Gromov-Witten potential functions of quintics. By using these structure theorems, we prove Yamaguchi-Yau’s Polynomial Ring Conjecture in this paper and prove Bershadsky-Cecotti-Ooguri-Vafa’s Feynman rule conjecture in the subsequent paper.


Huai-Liang Chang

Department of Mathematics, The Hong Kong University of Science and Technology, Hong Kong

Shuai Guo

School of Mathematical Sciences and Beijing International Center for Mathematical Research, Peking University, Beijing, China

Jun Li

Shanghai Center for Mathematical Sciences, Fudan University, Shanghai, China