VOA modules vs. bulk line operators in the 3d A/B-model

Determine and construct a precise correspondence between selected modules for the boundary vertex operator algebras V^A and V^B and bulk line operators in the 3d A- and B-models, respectively, specifying the objects on both sides and the functorial relationship that realizes this matching.

Background

Beyond local operators, the conjectural program relates boundary VOA representation theory to topological line operators in the bulk 3d TQFTs obtained by A- and B-twists. Establishing a concrete correspondence would deepen the link between algebraic structures on the boundary and topological defects in the bulk.

The authors note that parts of this program have been proven for abelian gauge theories, but the general module–line-operator correspondence remains conjectural, motivating further study.

References

It was further conjectured that certain modules for the boundary VOA would correspond to bulk line operators in $\mathcal{T}{A/B}$.

— $L_1(\mathfrak{psl}_{n|n})$ from BRST reductions, associated varieties and nilpotent orbits  (2409.13028 - Ferrari et al., 2024) in Section 1 (Introduction)

The result is that we determine the S-matrix from several non-trivial necessary conditions along with a conjectural map from UV Wilson lines to IR simple lines:

— The Gaiotto-Kim Trace Formula and Line Defects  (2609.24582 - Kim et al., 21 Sep 2026) in Section 3, subsection “Algorithm for determining the UV lines”