LG/CY Correspondence for Elliptic Orbifold Curves via Modularity

Yefeng Shen Stanford University Jie Zhou Perimeter Institute

Mathematical Physics mathscidoc:1608.22001

We prove the Landau-Ginzburg/Calabi-Yau correspondence between the Gromov-Witten theory of each elliptic orbifold curve and its Fan-Jarvis-Ruan-Witten theory counterpart via modularity. We show that the correlation functions in these two enumerative theories are different representations of the same set of quasi-modular forms, expanded around different points on the upper-half plane. We relate these two representations by the Cayley transform.
Landau-Ginzburg/Calabi-Yau correspondence, modularity
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  title={LG/CY Correspondence for Elliptic Orbifold Curves via Modularity},
  author={Yefeng Shen, and Jie Zhou},
Yefeng Shen, and Jie Zhou. LG/CY Correspondence for Elliptic Orbifold Curves via Modularity. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20160817202200101795218.
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