$\rm G_2$ holonomy manifolds are superconformal

TL;DR

This paper demonstrates that for manifolds with G_2 holonomy, the chiral de Rham complex's vertex algebra contains two commuting G_2 superconformal algebras, revealing deep algebraic structures linked to special holonomy.

Contribution

It proves the presence of two commuting G_2 superconformal algebras within the vertex algebra of the chiral de Rham complex on G_2 holonomy manifolds, using explicit computations.

Findings

Vertex algebra contains two commuting G_2 superconformal algebras.

Explicit computational proof of algebraic structures.

Reveals deep connection between G_2 holonomy and superconformal symmetry.

Abstract

We study the chiral de Rham complex (CDR) over a manifold $M$ with holonomy $\rm G_2$. 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.