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 superconformal vertex algebra associated to solutions of the Hull-Strominger system. The construction is via embeddings of the superconformal vertex algebra in the chiral de Rham complex of a string Courant algebroid. Our results require that the connection , 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 embedding.
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