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arXiv · 2305.06836

Vertex algebras from the Hull-Strominger system

Luis Álvarez-Cónsul·Andoni De Arriba de La Hera·Mario Garcia-Fernandez
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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.

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Luis Álvarez-Cónsul, Andoni De Arriba de La Hera, Mario Garcia-Fernandez. 2023-05-11. Vertex algebras from the Hull-Strominger system. https://arxiv.org/abs/2305.06836

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