Existence of the Rozansky–Witten (∞,3)-category RW

Establish the existence of a symmetric monoidal (∞,3)-category RW of Rozansky–Witten models in which objects are holomorphic symplectic manifolds, 1-morphisms include Lagrangian spans, and higher morphisms and compositions are governed by the push–pull formalism and mapping 2-categories predicted in Kapustin–Rozansky–Saulina’s framework. The goal is to realize the conjectured RW 3-category rigorously, beyond the current approximations such as CRW.

Background

The paper constructs a symmetric monoidal (∞,3)-category CRW that approximates the Rozansky–Witten 3-category proposed in the physics literature. Prior work has produced partial models: CHS (Calaque–Haugseng–Scheimbauer) built a semi-classical (∞,3)-category of iterated Lagrangian spans of symplectic derived stacks, while BCR and BCFR developed bicategorical models based on matrix factorizations. The full RW 3-category remains conjectural in the literature.

The authors explicitly reference the conjectural status of RW and motivate their construction as a commutative approximation, indicating that the complete noncommutative structure expected in RW (e.g., matrix factorization categories in homs) is not yet realized. This frames the existence and rigorous construction of RW as an explicit open problem.