Ekstrand–Heluani–Källén–Zabzine's Shatashvili–Vafa algebra conjecture for $G_{2}$-manifolds

Let $(M,g)$ be a $G_{2}$-manifold, let $\varphi$ be its corresponding defining $3$-form, and let $\Phi_{\pm}$ be the global sections of the chiral de Rham complex corresponding to $\varphi$. Set

$$K_{\pm}:=G_{(0)}\left(\Phi_{\pm}\right).$$

Shatashvili–Vafa algebra conjecture. The section pairs $\{\Phi_{+},K_{+}\}$ and $\{\Phi_{-},K_{-}\}$ generate two commuting copies of the Shatashvili–Vafa $G_{2}$ superconformal algebra.

This conjecture proposes that the chiral de Rham complex of a $G_{2}$-manifold contains two commuting copies of the $G_{2}$ superconformal algebra, providing the expected algebraic structure associated with $G_{2}$ holonomy and superconformal symmetry. The supplied text does not state whether the conjecture has been resolved.