Poisson Vertex Algebras and Three-Dimensional Gauge Theory
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866910838717153280 |
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| author | Khan, Ahsan Z. Zeng, Keyou |
| author_facet | Khan, Ahsan Z. Zeng, Keyou |
| contents | We introduce a mixed holomorphic-topological gauge theory in three dimensions associated to a (freely generated) Poisson vertex algebra. The $λ$-bracket of the PVA plays the role of the structure constants of the gauge algebra and the gauge invariance of the theory holds if and only if the $λ$-bracket Jacobi identity is satisfied. We show that the holomorphic-topological symmetry of the theory enhances to full topological symmetry if the Poisson vertex algebra contains a Virasoro element. We outline examples associated to PVAs of $\mathcal{W}$-type and demonstrate their connections to various versions of $3d$ gravity. We expect the three-dimensional Poisson sigma model to play an important role in the deformation quantization of Poisson vertex algebras. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_13227 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Poisson Vertex Algebras and Three-Dimensional Gauge Theory Khan, Ahsan Z. Zeng, Keyou High Energy Physics - Theory Quantum Algebra We introduce a mixed holomorphic-topological gauge theory in three dimensions associated to a (freely generated) Poisson vertex algebra. The $λ$-bracket of the PVA plays the role of the structure constants of the gauge algebra and the gauge invariance of the theory holds if and only if the $λ$-bracket Jacobi identity is satisfied. We show that the holomorphic-topological symmetry of the theory enhances to full topological symmetry if the Poisson vertex algebra contains a Virasoro element. We outline examples associated to PVAs of $\mathcal{W}$-type and demonstrate their connections to various versions of $3d$ gravity. We expect the three-dimensional Poisson sigma model to play an important role in the deformation quantization of Poisson vertex algebras. |
| title | Poisson Vertex Algebras and Three-Dimensional Gauge Theory |
| topic | High Energy Physics - Theory Quantum Algebra |
| url | https://arxiv.org/abs/2502.13227 |