Infinite Dimensional Topological-Holomorphic Symmetry in Three-Dimensions
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866917451659214848 |
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| author | Chen, Hank Liniado, Joaquin |
| author_facet | Chen, Hank Liniado, Joaquin |
| contents | We introduce a three-dimensional quantum field theory with an infinite-dimensional symmetry, realized explicitly through a centrally extended affine graded Lie algebra. This symmetry is a direct three-dimensional generalization of the chiral symmetry in the Wess-Zumino-Witten model. Upon performing radial quantization, we construct the Fock space of the theory and, via a three-dimensional analogue of the state-operator correspondence, we demonstrate that the algebra of local operators is endowed with the structure of a raviolo vertex algebra. Accordingly, this setup provides a framework for extending the methods of two-dimensional conformal field theory to three dimensions, and we expect it to lay the groundwork for exact methods in three-dimensional quantum field theory. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2507_01858 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Infinite Dimensional Topological-Holomorphic Symmetry in Three-Dimensions Chen, Hank Liniado, Joaquin High Energy Physics - Theory Mathematical Physics 81T45, 81T70, 81T40 We introduce a three-dimensional quantum field theory with an infinite-dimensional symmetry, realized explicitly through a centrally extended affine graded Lie algebra. This symmetry is a direct three-dimensional generalization of the chiral symmetry in the Wess-Zumino-Witten model. Upon performing radial quantization, we construct the Fock space of the theory and, via a three-dimensional analogue of the state-operator correspondence, we demonstrate that the algebra of local operators is endowed with the structure of a raviolo vertex algebra. Accordingly, this setup provides a framework for extending the methods of two-dimensional conformal field theory to three dimensions, and we expect it to lay the groundwork for exact methods in three-dimensional quantum field theory. |
| title | Infinite Dimensional Topological-Holomorphic Symmetry in Three-Dimensions |
| topic | High Energy Physics - Theory Mathematical Physics 81T45, 81T70, 81T40 |
| url | https://arxiv.org/abs/2507.01858 |