Landau–Ginzburg/Calabi–Yau correspondence for quintic three-folds via symplectic transformations

By A. Chiodo, Y. Ruan. 2008

134 citations recorded by the source corpus.

We compute the recently introduced Fan–Jarvis–Ruan–Witten theory of W-curves in genus zero for quintic polynomials in five variables and we show that it matches the Gromov–Witten genus-zero theory of the quintic three-fold via a symplectic transformation. More specifically, we show that the J-function encoding the Fan–Jarvis–Ruan–Witten theory on the A-side equals via a mirror map the I-function embodying the period integrals at the Gepner point on the B-side. This identification inscribes the physical Landau–Ginzburg/Calabi–Yau correspondence within the enumerative geometry of moduli of curves, matches the genus-zero invariants computed by the physicists Huang, Klemm, and Quackenbush at the Gepner point, and yields via Givental’s quantization a prediction on the relation between the full higher genus potential of the quintic three-fold and that of Fan–Jarvis–Ruan–Witten theory.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/f610ee8c6af250b9f45e30d6672687a473f393a3

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Citations in the corpus

Equivalence of ELSV and Bouchard–Mariño conjectures for $$r$$r-spin Hurwitz numbers (2013, methodology): “This fact has been observed in [10] in the presence of Witten’s class, then in [9] in the setting we use here.”
Homological mirror symmetry for Brieskorn–Pham singularities (2009, methodology): “If we choose G = 〈J〉, then Calabi-Yau/Landau-Ginzburg correspondence predicts a relation between Gromov-Witten invariants of the quintic 3-fold and by Fan-Jarvis-RuanWitten invariants of (W, 〈J〉), which is proved by Chiodo and Ruan [2].”
Matrix factorizations and Cohomological Field Theories (2011, methodology): “ce as an R-module via the G-grading given by γ′. The component corresponding to γ′ = 1 admits a certain twist by a Todd class, and conjecturally this reduced CohFT is isomorphic to the FJR-theory. In [10] the FJR-theory for the quintic threefold is related to a certain specialization of the correspo”