English

Vertex algebras from the Hull-Strominger system

Differential Geometry 2024-03-05 v2 High Energy Physics - Theory Algebraic Geometry Quantum Algebra

Abstract

Motivated by the programme on mirror symmetry for non-K\"ahler manifolds, we construct representations of the N=2N=2 superconformal vertex algebra associated to solutions of the Hull-Strominger system. The construction is via embeddings of the N=2N=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=2N=2 embedding.

Keywords

Cite

@article{arxiv.2305.06836,
  title  = {Vertex algebras from the Hull-Strominger system},
  author = {Luis Álvarez-Cónsul and Andoni De Arriba de La Hera and Mario Garcia-Fernandez},
  journal= {arXiv preprint arXiv:2305.06836},
  year   = {2024}
}

Comments

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

R2 v1 2026-06-28T10:32:04.467Z