Vertex algebras from the Hull-Strominger system

Abstract

Motivated by the programme on mirror symmetry for non-Kähler manifolds, we construct representations of the $N=2$ superconformal vertex algebra associated to solutions of the Hull-Strominger system. The construction is via embeddings of the $N=2$ superconformal vertex algebra in the chiral de Rham complex of a string Courant algebroid. Our results require that the connection $\nabla$, one of the unknowns of the system, is Hermitian-Yang-Mills. Our main theorem proves that any solution of the Hull-Strominger system satisfying this condition has an associated $N=2$ embedding.

72 pages. Improved versions of the main results, which remove the hypothesis on the torsion bivector. In particular, Conjecture 1.2 in the previous version is settled in the affirmative