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arXiv · 2312.16278

Twisted restricted conformal blocks of vertex operator algebras I: $g$-twisted correlation functions and fusion rules

Xu Gao·Jianqi Liu·Yiyi Zhu
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Abstract

In this paper, we introduce a notion of $g$-twisted restricted conformal block on the three-pointed twisted projective line $\mathfrak{x}\colon\overline{C}\to\mathbb{P^1}$ associated with an untwisted module $M^1$ and the bottom levels of two $g$-twisted modules $M^2$ and $M^3$ over a vertex operator algebra $V$. We show that the space of twisted restricted conformal blocks is isomorphic to the space of $g$-twisted (restricted) correlation functions defined by the same datum and to the space of intertwining operators among these twisted modules. As an application, we derive a twisted version of the Fusion Rules Theorem.

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Xu Gao, Jianqi Liu, Yiyi Zhu. 2023-12-26. Twisted restricted conformal blocks of vertex operator algebras I: $g$-twisted correlation functions and fusion rules. https://doi.org/10.1016/j.jalgebra.2025.03.013

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