Large $N$ Vertex Algebras via Deligne Category
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866915611341225984 |
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| author | Zeng, Keyou |
| author_facet | Zeng, Keyou |
| contents | In this paper, we propose a new construction of vertex algebras using the Deligne category. This approach provides a rigorous framework for defining the so-called large $N$ vertex algebra, which has appeared in recent physics literatures. We first define the notion of a vertex algebra in a symmetric monoidal category and extend familiar constructions in ordinary vertex algebras to this broader categorical context. As an application, we consider a $βγ$ vertex algebra in the Deligne category and construct the large N vertex algebra from it. We study some simple properties of this vertex algebra and analyze a certain vertex Poisson algebra limit. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_03004 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Large $N$ Vertex Algebras via Deligne Category Zeng, Keyou Quantum Algebra High Energy Physics - Theory Mathematical Physics In this paper, we propose a new construction of vertex algebras using the Deligne category. This approach provides a rigorous framework for defining the so-called large $N$ vertex algebra, which has appeared in recent physics literatures. We first define the notion of a vertex algebra in a symmetric monoidal category and extend familiar constructions in ordinary vertex algebras to this broader categorical context. As an application, we consider a $βγ$ vertex algebra in the Deligne category and construct the large N vertex algebra from it. We study some simple properties of this vertex algebra and analyze a certain vertex Poisson algebra limit. |
| title | Large $N$ Vertex Algebras via Deligne Category |
| topic | Quantum Algebra High Energy Physics - Theory Mathematical Physics |
| url | https://arxiv.org/abs/2503.03004 |