Critical-level duality conjecture for regular \mathcal{W}-superalgebras

Assume $n\geqslant m$, and let $\kappa_c$ denote the critical level. Let $\mathcal{A}^m_{\mathrm{deg}}$ be the degenerate $\beta\gamma$-system associated with $\mathbb{C}^m\oplus\overline{\mathbb{C}}^m$, let $\mathcal{F}_{n|m}$ be as above, and let $\mathrm{GL}_m$ act diagonally. Critical-level duality conjecture. There is an isomorphism of vertex superalgebras

$$\mathcal{W}^{\kappa_c}(\mathfrak{gl}_{n|m})\simeq\mathbb{C}[J_\infty\mathbb{A}^{n-m}]\otimes(\mathcal{A}^m_{\mathrm{deg}}\otimes\mathcal{F}_{n|m})^{\mathrm{GL}_m}.$$

This is the critical-level analogue of Ito's conjectural duality, obtained by interpreting the dual level as $\check{\kappa}=\infty$ and replacing the corresponding $\mathcal{W}$-algebra by the Poisson vertex algebra of functions on the jet scheme of the relevant Slodowy slice.