Vertex algebras from the Hull-Strominger system

2023/05/11 by Luis Álvarez-Cónsul, Álvarez-Cónsul, Luis, Andoni De Arriba de La Hera +3 · 1 citation
Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #Algebraic Geometry (math.AG) #Algebraic structures and combinatorial models #Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Nonlinear Waves and Solitons #Quantum Algebra (math.QA)

paper · pdf · doi:10.48550/arxiv.2305.06836

openalex publication_date 2023/05/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 ∇, 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.

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