Genus-zero Permutation-twisted Conformal Blocks for Tensor Product Vertex Operator Algebras: The Tensor-factorizable Case
Fuente:
arXiv
Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2021
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866914259444695040 |
|---|---|
| author | Gui, Bin |
| author_facet | Gui, Bin |
| contents | For a vertex operator algebra $V$, we construct an explicit isomorphism between the space of genus-0 conformal blocks associated to permutation-twisted $V^{\otimes n}$-modules and the space of conformal blocks associated to untwisted $V$-modules and a branched covering C of the Riemann sphere. As a consequence, when V is CFT-type, rational, and C2 cofinite, the fusion rules for permutation-twisted modules are determined. We also relate the sewing and factorization of permutation-twisted $V^{\otimes n}$-conformal blocks and untwisted $V$-conformal blocks. Various applications are discussed.
Note the differences in theorem and equation numbering between the arXiv version and the published version. Some terminology also varies: See Def. 2.2.1 (Def. 2.20 of the published version) for a slight difference in the meanings of $\mathbb U$. The term "Analytic Jacobi identity" in the arXiv version is called the "duality property" in the published version. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2111_04662 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Genus-zero Permutation-twisted Conformal Blocks for Tensor Product Vertex Operator Algebras: The Tensor-factorizable Case Gui, Bin Quantum Algebra Mathematical Physics For a vertex operator algebra $V$, we construct an explicit isomorphism between the space of genus-0 conformal blocks associated to permutation-twisted $V^{\otimes n}$-modules and the space of conformal blocks associated to untwisted $V$-modules and a branched covering C of the Riemann sphere. As a consequence, when V is CFT-type, rational, and C2 cofinite, the fusion rules for permutation-twisted modules are determined. We also relate the sewing and factorization of permutation-twisted $V^{\otimes n}$-conformal blocks and untwisted $V$-conformal blocks. Various applications are discussed. Note the differences in theorem and equation numbering between the arXiv version and the published version. Some terminology also varies: See Def. 2.2.1 (Def. 2.20 of the published version) for a slight difference in the meanings of $\mathbb U$. The term "Analytic Jacobi identity" in the arXiv version is called the "duality property" in the published version. |
| title | Genus-zero Permutation-twisted Conformal Blocks for Tensor Product Vertex Operator Algebras: The Tensor-factorizable Case |
| topic | Quantum Algebra Mathematical Physics |
| url | https://arxiv.org/abs/2111.04662 |