A Landau–Ginzburg mirror theorem via matrix factorizations

Abstract

Abstract For an invertible quasihomogeneous polynomial 𝒘 {{\boldsymbol{w}}} we prove an all-genus mirror theorem relating two cohomological field theories of Landau–Ginzburg type. On the B-side it is the Saito–Givental theory for a specific choice of a primitive form. On the A-side, it is the matrix factorization CohFT for the dual singularity 𝒘 T {{\boldsymbol{w}}^{T}} with the maximal diagonal symmetry group.