Higher categories of push-pull spans, II: Matrix factorizations

This is the second part of a project aimed at formalizing Rozansky-Witten models in the functorial field theory framework. In the first part we constructed a symmetric monoidal (, 3) -category CRW of commutative Rozansky-Witten models with the goal of approximating the 3-category of Kapustin and Rozansky. In this paper we extend work of Brunner, Carqueville, Fragkos, and Roggenkamp on the affine Rozansky-Witten models: we exhibit a functor connecting their 2-category of matrix factorizations with the homotopy 2-category of CRW, and calculate the associated TFTs.