Landau-Ginzburg/Calabi-Yau correspondence, global mirror symmetry and Orlov equivalence

Understand

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 ideas of Witten.

• Moreover, on both sides, we highlight two remarkable integral local systems arising from the common formalism of 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.