零 genus 的置换扭曲共形块：张量积顶点算子代数的共形块：张量可分解情况
Genus-zero Permutation-twisted Conformal Blocks for Tensor Product Vertex Operator Algebras: The Tensor-factorizable Case
AI总结：
本文研究了张量积顶点算子代数的零 genus 置换扭曲共形块，通过构造同构关系确定了有理性和 C2 共穷条件下的融合规则，并探讨了共形块的缝合与分解。
摘要：
对于一个顶点算子代数 $V$，我们构造了一个显式同构，将 genus-0 共形块空间（关联于置换扭曲 $V^{\otimes n}$-模）与共形块空间（关联于未扭曲 $V$-模和一个分支覆盖 C 的黎曼球面）之间建立联系。作为结果，当 V 是 CFT 类型、有理性和 C2 共穷时，置换扭曲模的融合规则被确定。我们还讨论了置换扭曲 $V^{\otimes n}$-共形块与未扭曲 $V$-共形块的缝合和分解。讨论了各种应用。注意 arXiv 版本与发表版本之间定理和方程编号的不同。一些术语也有所不同：参见定义 2.2.1（发表版本的定义 2.20）以了解 $\mathbb U$ 的含义的细微差别。arXiv 版本中的术语“解析雅可比恒等式”在发表版本中称为“对称性性质”.
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
