The de Rham quantum global geometric Langlands conjecture

Let $G$ be a simple reductive group, let $\check{G}$ be its Langlands dual group, let $\check{h}$ be the dual Coxeter number of $G$, and let $r$ be the maximal multiplicity of arrows in the Dynkin diagram of $G$. For every $c\in k$, let $\operatorname{DMod}_c(\operatorname{Bun}_G)$ denote the derived category of $D$-modules twisted by the $\frac{c-\check{h}}{2\check{h}}$-th power of the determinant line bundle $\mathcal L_{\det}$ on $\operatorname{Bun}_G$. The de Rham quantum global geometric Langlands conjecture. There exists a canonical equivalence of derived categories

$$\operatorname{DMod}_c(\operatorname{Bun}_G)\xrightarrow[\cong]{\mathbb L_c}\operatorname{DMod}_{-\frac{1}{rc}}(\operatorname{Bun}_{\check{G}}).$$

At the limit $c\tilde{o}0$, the conjecture is expected to recover the ordinary global geometric Langlands correspondence, while unlike that correspondence it is symmetric in $G$ and $\check{G}$.