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PreprintCC BY 4.0arXiv

Crossed modularity of twisted VOA modules

  • Shun Xu
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Abstract

Let V be a strongly rational vertex operator algebra and G≤Aut(V) a finite group. Using the G-crossed braided fusion structure of twisted modules constructed in \cite{Crossed}, we prove that the conformal twist e2πiL(0) gives a crossed ribbon structure and that the crossed category is modular in Kirillov's sense. Consequently, its equivariantization is a modular tensor category. We also obtain dimension and simple-object counting formulas for the twisted sectors.

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Cite

BibTeXRIS
BibTeX
@misc{xu2026crossed,
  title = {{Crossed modularity of twisted VOA modules}},
  author = {Shun Xu},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.34193},
  eprint = {2610.34193},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.34193},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Crossed modularity of twisted VOA modules
AU  - Shun Xu
PY  - 2026
DA  - 2026/10/25
PB  - arXiv
DO  - 10.48550/arxiv.2610.34193
UR  - https://arxiv.org/abs/2610.34193
AB  - Let V be a strongly rational vertex operator algebra and G≤Aut(V) a finite group. Using the G-crossed braided fusion structure of twisted modules constructed in \cite{Crossed}, we prove that the conformal twist e^2πiL(0) gives a crossed ribbon structure and that the crossed category is modular in Kirillov's sense. Consequently, its equivariantization is a modular tensor category. We also obtain dimension and simple-object counting formulas for the twisted sectors.
ER  -