Ext-algebra of the boundary VOA tensor unit vs. local operator ring of the 3d A/B-model

Establish that, provided the boundary condition supports enough local operators, the derived endomorphism algebra of the tensor unit in a suitable category of modules for the boundary vertex operator algebras V^A and V^B is isomorphic to the ring of local operators of the respective 3d A- and B-model TQFT, thereby identifying it with the algebras of functions on the Coulomb and Higgs branches, respectively.

Background

The paper studies boundary VOAs arising from the 3d A- and B-models of supersymmetric gauge theories and how they encode the geometry of Coulomb and Higgs branches. Prior works proposed a categorical link between boundary VOAs and bulk local operators: specifically, that the Ext-algebra of the tensor unit in an appropriate module category over the boundary VOA reconstructs the bulk local operator algebra.

While aspects of this conjecture have been proven for abelian gauge theories (including SQED[n]) in cited work, the general statement remains conjectural beyond those cases, and the authors restate the conjecture to frame their results.