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PreprintCC BY 4.0arXiv

Equivalence between rationality and modular invariance under C2-cofiniteness

  • Hao Wang
  • Jiang Yang
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Abstract

We prove that for a simple and C2-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}.

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Cite

BibTeXRIS
BibTeX
@misc{wang2026equivalence,
  title = {{Equivalence between rationality and modular invariance under $C_2$-cofiniteness}},
  author = {Hao Wang and Jiang Yang},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.36565},
  eprint = {2610.36565},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.36565},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Equivalence between rationality and modular invariance under C_2-cofiniteness
AU  - Hao Wang
AU  - Jiang Yang
PY  - 2026
DA  - 2026/10/27
PB  - arXiv
DO  - 10.48550/arxiv.2610.36565
UR  - https://arxiv.org/abs/2610.36565
AB  - 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}.
ER  -