Equivariant homological mirror symmetry for torus fibrations

Let $X\to B$ be a Lagrangian torus fibration with a compatible action of a finite group $G$, let $Y$ be its mirror, and let $W:Y\to\mathbb{C}$ be the resulting Landau–Ginzburg potential. Write $\mathcal{F}uk_G^s(X)$ for the derived $s$-orbifolded Fukaya category, $\mathcal{FS}_G^s(Y,W)$ for the derived equivariant Fukaya–Seidel category, $\operatorname{Coh}_G(X)$ for the category of $G$-equivariant coherent sheaves, and $MF_G(W)$ for the $G$-equivariant matrix factorization category.

Equivariant torus-fibration mirror-symmetry conjecture. There should be equivalences

$$D^b\mathcal{F}uk_G^s(X)\cong D^bMF_G(W),$$ $$D^b\mathcal{FS}_G^s(Y,W)\cong D^b\operatorname{Coh}_G(X).$$

The character group $\widehat{G}$ acts compatibly on both sides by twisting equivariant structures.

This formulates homological mirror symmetry in the presence of a compatible finite-group action and incorporates the spin profile of the torus fibers. The source gives no resolution status.