${\mathrm{G}}_2$ holonomy manifolds are superconformal

We study the chiral de Rham complex (CDR) over a manifold $M$ with holonomy ${\mathrm{G}}_2$. We prove that the vertex algebra of global sections of the CDR associated to $M$ contains two commuting copies of the Shatashvili-Vafa $\rm G_2$ superconformal algebra. Our proof is a tour de force, based on explicit computations.