Landau-Ginzburg/Calabi-Yau correspondence, global mirror symmetry and Orlov equivalence
TL;DR: In this article, the Gromov-Witten theory of Calabi-Yau hypersurfaces matches, in genus zero and after an analytic continuation, the quantum singularity theory (FJRW theory) recently introduced by Fan, Jarvis and Ruan following a proposal of Witten.
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Abstract: We show that the Gromov-Witten theory of Calabi-Yau hypersurfaces matches, in genus zero and after an analytic continuation, the quantum singularity theory (FJRW theory) recently introduced by Fan, Jarvis and Ruan following a proposal of Witten. Moreover, on both sides, we highlight two remarkable integral local systems arising from the common formalism of \(\widehat {\Gamma }\)-integral structures applied to the derived category of the hypersurface {W=0} and to the category of graded matrix factorizations of W. In this setup, we prove that the analytic continuation matches Orlov equivalence between the two above categories.
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Citations
A mathematical theory of the gauged linear sigma model
TL;DR: In this paper, a mathematical theory of Witten's GLSM is presented, which applies to a wide range of examples, including many cases with nonabelian gauge groups.
101
A Mathematical Theory of the Gauged Linear Sigma Model
TL;DR: In this paper, a mathematical theory of Witten's GLSM is presented, which applies to a wide range of examples, including many cases with non-Abelian gauge groups.
82
•Posted Content
BCFG Drinfeld-Sokolov Hierarchies and FJRW-Theory
TL;DR: In this paper, Fan, Jarvis and Ruan proved that the total descendant potential of the FJRW invariants of an ADE singularity is a tau function of the corresponding mirror ADE Drinfeld-Sokolov hierarchy.
42
Wall-crossing in genus zero Landau-Ginzburg theory
Dustin Ross,Yongbin Ruan +1 more
TL;DR: In this paper, the authors studied genus zero wall-crossing for a family of moduli spaces introduced by Fan-Farvis-Ruan, and showed that they all lie on the same Lagrangian cone associated to the Fan-Jarvis Ruan Witten theory of W.
31
•Posted Content
Global mirror symmetry for invertible simple elliptic singularities
Todor Milanov,Yefeng Shen +1 more
TL;DR: In this paper, the Saito-Givental theory of a simple elliptic singularity is shown to be mirror to either the Gromov-Witten theory of an elliptic orbifold or the Fan-Jarvis-Ruan-Wenn theory of invertible simple singularity with diagonal symmetries.
23
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