Year: 2026
Type: preprint
Abstract: We prove that for a simple and $C_2$-cofinite vertex operator algebra, the rationality is equivalent to the modular invariance of the space of complete ordinary one-point trace functions of its irreducible modules. This proves a conjecture given by Dong-Ren in \cite{DongRen}, which is also the inverse theorem of Zhu's modular invariance theorem \cite{Zhu}.
Source: arXiv (Cornell University)
Authors: Wang, Hao, Yang, Jiang
Institutions: Northwest University, Guangxi Minzu University
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Award: G254172227
OpenAlex ID: W7224136243