The torus 3D B-model Fukaya–IndCoh equivalence conjecture

Let $T$ be a torus, let $\mathfrak{t}$ be its Lie algebra, and let $T^{\vee}_{\mathbb{C}}$ be the complex dual torus. Let $\mathrm{BFM}(T^{\vee})$ denote the associated BFN space. Torus Fukaya–IndCoh equivalence conjecture. There is an equivalence of $2$-categories

$${}^{2}\mathrm{Fuk}([\mathfrak{t}^{*}/T])\simeq \mathrm{IndCohShvCat}(T^{\vee}_{\mathbb{C}}),$$

and the Hochschild cohomology $1$-categories of these $2$-categories are equivalent to

$$\operatorname{QCoh}(\mathrm{BFM}(T^{\vee})).$$

This is proposed as an identification of the shifted Fukaya-theoretic and Ind-coherent models for the 3D B-model in the torus case; the conjecture remains open.