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Vertex algebras from the Hull-Strominger system

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arxiv 2305.06836 v2 pith:OKV7LB5S submitted 2023-05-11 math.DG hep-thmath.AGmath.QA

classification math.DGhep-thmath.AGmath.QA
keywords systemhull-stromingervertexalgebraassociatedsuperconformalahleralgebras
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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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Cited by 3 Pith papers

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