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

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.