Genus-One Gromov–Witten Invariants of Quintic Three-folds via MSP Localization. (16th August 2018)

• Record Type: Journal Article
• Authors: Chang, Huai-Liang; Guo, Shuai; Li, Wei-Ping; Zhou, Jie
• Is Part Of: International mathematics research notices. Volume 2020:Number 19(2020)
• Page Start: 6421
• Page End: 6462
• Publication Date: 2018-08-16
• Subjects: Mathematics -- Periodicals; 510
• DOI: 10.1093/imrn/rny201
• Languages: English
• ISSNs: 1073-7928

Abstract

Abstract: The moduli stack of Mixed Spin P-fields (MSP) provides an effective algorithm to evaluate all genus Gromov–Witten (GW) invariants of the quintic Calabi–Yau (CY) three-folds. This paper is to apply the algorithm to the genus-one case. We use the localization formula, the proposed algorithm in [ 10, 11 ], and Zinger's packaging technique to compute the genus-one GW invariants of the quintic CY three-folds. Our approach to the formula suggests a correspondence between each type of MSP graphs with each physics' phase: CY, Landau–Ginzburg, or conifold point. In this process, new differential relations among Givental's I-functions are also discovered.