Categorical Saito theory, I: A comparison result

In this paper, we present an explicit cyclic minimal $A_{\mathrm{\infty }}$ model for the category of matrix factorizations $\text{MF}(W)$ 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 $\text{MF}(W)$ is isomorphic to Saito’s original geometric construction in primitive form theory. An immediate corollary of this comparison result is that the analogue of Caldararu’s conjecture holds for the category $\text{MF}(W)$.