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

TL;DR

This paper extends the formalization of Rozansky-Witten models within a higher category framework, connecting matrix factorizations to functorial field theories and computing related topological field theories.

Contribution

It constructs a functor linking matrix factorizations to a higher category of Rozansky-Witten models, advancing the categorical understanding of these models.

Findings

Established a functor from matrix factorizations to the homotopy 2-category of $\

$-category of models.

Calculated the associated topological field theories.

Abstract

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 $(\infty, 3)$-category $\mathscr{CRW}$ 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 $\mathscr{CRW}$, and calculate the associated TFTs.