The Spin(7) global-section conjecture for the chiral de Rham complex

Let $M$ be an $8$-dimensional Riemannian manifold with holonomy $Spin_7$, and let $\Omega^{ch}_M$ denote its chiral de Rham complex. Write $C^\infty(M,\Omega^{ch}_M)$ for the associated vertex algebra, and let $SVSpin_7$ denote the relevant superconformal vertex algebra with central charge $c=12$. Spin(7) global-section conjecture. The vertex algebra $C^\infty(M,\Omega^{ch}_M)$ carries two global sections $X^+$ and $X^-$ generating two commuting copies of $SVSpin_7$ of central charge $c=12$. This predicts that the holonomy-induced structure on the chiral de Rham complex extends globally in the $Spin(7)$ case; the supplied text does not state whether the conjecture has been proved or remains open.