Landau-Ginzburg/Calabi-Yau correspondence for a complete intersection via matrix factorizations

TL;DR

This paper extends the Landau-Ginzburg/Calabi-Yau correspondence to complete intersections, linking derived categories and quantum invariants through matrix factorizations and singularity theory.

Contribution

It generalizes the known hypersurface correspondence to complete intersections, establishing a direct relation via Chen character and matrix factorizations.

Findings

Established equivalence between quantum invariants and Gromov-Witten invariants for complete intersections.

Connected derived category equivalences with matrix factorizations of singularities.

Extended Chiodo-Iritani-Ruan's theorem to a broader class of Calabi-Yau varieties.

Abstract

By generalizing the Landau-Ginzburg/Calabi-Yau correspondence for hypersurfaces, we can relate a Calabi-Yau complete intersection to a hybrid Landau-Ginzburg model: a family of isolated singularities fibered over a projective line. In recent years Fan, Jarvis, and Ruan have defined quantum invariants for singularities of this type, and Clader and Clader-Ross have provided a equivalence between these invariants and Gromov-Witten invariants of complete intersections. For Calabi-Yau complete intersections of two cubics, we show that this equivalence is directly related - via Chen character - to the equivalences between the derived category of coherent sheaves and that of matrix factorizations of the singularities. This generalizes Chiodo-Iritani-Ruan's theorem matching Orlov's equivalences and quantum LG/CY correspondence for hypersurfaces.