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

2023/12/26 by Xu Gao, Gao, Xu, Jianqi Liu +3
Mathematics · #17B69 #81T40 #Advanced Operator Algebra Research #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Quantum Algebra (math.QA)

paper · pdf · doi:10.48550/arxiv.2312.16278

openalex publication_date 2023/12/26 · openalex created_date 2023/12/30 · openalex updated_date 2026/07/28

Abstract

In this paper, we introduce a notion of g-twisted restricted conformal block on the three-pointed twisted projective line \mathfrakx\colonC→\mathbbP¹ associated with an untwisted module M¹ and the bottom levels of two g-twisted modules M² and M³ 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.

Related

• Twisted restricted conformal blocks of vertex operator algebras II: twisted restricted conformal blocks on totally ramified orbicurves
• Twist vertex operators for twisted modules
• Twisted Modules over Vertex Algebras on Algebraic Curves
• Applications of the factorization theorem of conformal blocks to vertex operator algebras
• Twisted associative algebras associated to vertex algebras