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PreprintarXiv licencearXiv

Reverse Module Categories of Vertex Operator Algebras

  • Chongying Dong
  • Binghui Li
  • Li Ren
  • Yilong Wang
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Abstract

We study the realization of the reverse braided category of the module category of a rational vertex operator algebra V. Using holomorphic extensions and commutant constructions, we prove that this realization property is preserved under suitable cosets, tensor products, extensions, and finite-group orbifolds. As applications, we establish the property for unitary Virasoro minimal models, affine vertex operator algebras of types ABCDE at positive integral levels, the corresponding principal W-algebras of type ADE, and related parafermion vertex operator algebras.

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Cite

BibTeXRIS
BibTeX
@misc{dong2026reverse,
  title = {{Reverse Module Categories of Vertex Operator Algebras}},
  author = {Chongying Dong and Binghui Li and Li Ren and Yilong Wang},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.26907},
  eprint = {2610.26907},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.26907},
}
RIS
TY  - UNPB
TI  - Reverse Module Categories of Vertex Operator Algebras
AU  - Chongying Dong
AU  - Binghui Li
AU  - Li Ren
AU  - Yilong Wang
PY  - 2026
DA  - 2026/10/28
PB  - arXiv
DO  - 10.48550/arxiv.2610.26907
UR  - https://arxiv.org/abs/2610.26907
AB  - We study the realization of the reverse braided category of the module category of a rational vertex operator algebra V. Using holomorphic extensions and commutant constructions, we prove that this realization property is preserved under suitable cosets, tensor products, extensions, and finite-group orbifolds. As applications, we establish the property for unitary Virasoro minimal models, affine vertex operator algebras of types ABCDE at positive integral levels, the corresponding principal W-algebras of type ADE, and related parafermion vertex operator algebras.
ER  -