Vertex algebras from the Hull-Strominger system

TL;DR

This paper constructs representations of the N=2 superconformal vertex algebra from solutions to the Hull-Strominger system, linking complex geometry, string theory, and vertex algebras in non-Kähler manifolds.

Contribution

It provides a novel method to embed the N=2 superconformal vertex algebra into the chiral de Rham complex for solutions of the Hull-Strominger system with Hermitian-Yang-Mills connection.

Findings

Established an N=2 embedding for solutions with Hermitian-Yang-Mills connection.

Connected Hull-Strominger system solutions to vertex algebra representations.

Extended mirror symmetry considerations to non-Kähler manifolds.

Abstract

Motivated by the programme on mirror symmetry for non-K\"ahler 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.