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PreprintarXiv licencearXiv

C2-Cofiniteness of Permutation Orbifolds I: Relative C1 Descent

  • Yuhan Gu
  • Jiancai Sun
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Abstract

We establish a relative C1-cofiniteness criterion for C2-cofiniteness of finite group orbifolds. For permutation actions on a simple, self contragredient, C2-cofinite vertex operator algebra of CFT type, it suffices to check a single relation for a derivative of the conformal vector in the Virasoro vertex operator algebra. This reduces the problem to a calculation depending only on the central charge and tensor degree. An exact calculation then proves cofiniteness for a family of nonsolvable permutation orbifolds without restricting the central charge.

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Cite

BibTeXRIS
BibTeX
@misc{gu2026c2cofiniteness,
  title = {{$C_2$-Cofiniteness of Permutation Orbifolds I: Relative $C_1$ Descent}},
  author = {Yuhan Gu and Jiancai Sun},
  howpublished = {arXiv},
  year = {2026},
  month = nov,
  doi = {10.48550/arxiv.2611.06201},
  eprint = {2611.06201},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2611.06201},
}
RIS
TY  - UNPB
TI  - C_2-Cofiniteness of Permutation Orbifolds I: Relative C_1 Descent
AU  - Yuhan Gu
AU  - Jiancai Sun
PY  - 2026
DA  - 2026/11/04
PB  - arXiv
DO  - 10.48550/arxiv.2611.06201
UR  - https://arxiv.org/abs/2611.06201
AB  - We establish a relative C_1-cofiniteness criterion for C_2-cofiniteness of finite group orbifolds. For permutation actions on a simple, self contragredient, C_2-cofinite vertex operator algebra of CFT type, it suffices to check a single relation for a derivative of the conformal vector in the Virasoro vertex operator algebra. This reduces the problem to a calculation depending only on the central charge and tensor degree. An exact calculation then proves cofiniteness for a family of nonsolvable permutation orbifolds without restricting the central charge.
ER  -