One-Point Restricted Conformal Blocks and the Fusion Tensor Product
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866912798702829568 |
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| author | Liu, Jianqi |
| author_facet | Liu, Jianqi |
| contents | We investigate a one-point restriction of conformal blocks on $(\mathbb{P}^1,\infty,1,0)$ associated with modules over a vertex operator algebra. By restricting the module attached to the point $\infty$ to its bottom degree, we obtain a new formula for computing fusion rules in terms of a left $A(V)$-module $M^1\odot M^2$ over the Zhu algebra $A(V)$. As a consequence, for strongly rational VOAs, the construction of $M^1\odot M^2$ induces the fusion tensor product on the module category $\mathsf{Mod}(A(V))$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_06313 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | One-Point Restricted Conformal Blocks and the Fusion Tensor Product Liu, Jianqi Quantum Algebra Mathematical Physics 17B69, 17B81, 81R10 We investigate a one-point restriction of conformal blocks on $(\mathbb{P}^1,\infty,1,0)$ associated with modules over a vertex operator algebra. By restricting the module attached to the point $\infty$ to its bottom degree, we obtain a new formula for computing fusion rules in terms of a left $A(V)$-module $M^1\odot M^2$ over the Zhu algebra $A(V)$. As a consequence, for strongly rational VOAs, the construction of $M^1\odot M^2$ induces the fusion tensor product on the module category $\mathsf{Mod}(A(V))$. |
| title | One-Point Restricted Conformal Blocks and the Fusion Tensor Product |
| topic | Quantum Algebra Mathematical Physics 17B69, 17B81, 81R10 |
| url | https://arxiv.org/abs/2411.06313 |