Associated-variety conjecture for boundary VOAs of abelian A-models

Let a three-dimensional abelian gauge theory be equipped with the A-twist and additional boundary free fermions, and let $V^A$ be the resulting boundary VOA. Write $X_{V^A}$ for its associated variety, and let the Higgs branch denote the holomorphic symplectic quotient associated with the theory. The associated-variety conjecture. There is an isomorphism

$$X_{V^A}\cong\text{the Higgs branch of the theory}.$$

The conjecture is motivated by free-field and BRST-reduction constructions and would imply that chiralisation commutes with reduction in these examples; its general status is not resolved in the source.