The hybrid Landau-Ginzburg models of Calabi-Yau complete intersections

TL;DR

This paper introduces a new cohomology framework for hybrid Landau-Ginzburg models, establishing an explicit isomorphism with the cohomology of Calabi-Yau complete intersections in weighted projective spaces, generalizing previous hypersurface results.

Contribution

It defines the cohomology of hybrid Landau-Ginzburg models and generalizes the combinatorial methods for hypersurfaces to complete intersections using orbifold cohomology techniques.

Findings

Established an explicit isomorphism between hybrid Landau-Ginzburg cohomology and Calabi-Yau complete intersection cohomology.

Generalized the combinatorial approach from hypersurfaces to complete intersections.

Streamlined the proof using orbifold Thom isomorphism and Tate twist.

Abstract

We observe that the state space of Landau-Ginzburg isolated singularities is simply a special case of Chen-Ruan orbifold cohomology relative to the generic fibre of the potential. This leads to the definition of the cohomology of hybrid Landau-Ginzburg models and its identification via an explicit isomorphism to the cohomology of Calabi-Yau complete intersections inside weighted projective spaces. The combinatorial method used in the case of hypersurfaces proven by the first named author in collaboration with Ruan is streamlined and generalised after an orbifold version of the Thom isomorphism and of the Tate twist.