Vertex algebras from the Hull-Strominger system
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866929263353004032 |
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| author | Álvarez-Cónsul, Luis de La Hera, Andoni De Arriba Garcia-Fernandez, Mario |
| author_facet | Álvarez-Cónsul, Luis de La Hera, Andoni De Arriba Garcia-Fernandez, Mario |
| contents | 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 $\nabla$, 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2305_06836 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Vertex algebras from the Hull-Strominger system Álvarez-Cónsul, Luis de La Hera, Andoni De Arriba Garcia-Fernandez, Mario Differential Geometry High Energy Physics - Theory Algebraic Geometry Quantum Algebra 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 $\nabla$, 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. |
| title | Vertex algebras from the Hull-Strominger system |
| topic | Differential Geometry High Energy Physics - Theory Algebraic Geometry Quantum Algebra |
| url | https://arxiv.org/abs/2305.06836 |