Categorical Saito theory, I: A comparison result

Abstract

In this paper, we present an explicit cyclic minimal A∞ model for the category of matrix factorizations MF(W) of an isolated hypersurface singularity. The key observation is to use Kontsevich's deformation quantization technique. Pushing this idea further, we use the Tsygan formality map to obtain a comparison theorem that the categorical Variation of Semi-infinite Hodge Structure of MF(W) is isomorphic to Saito's original geometric construction in primitive form theory.