PIRSA:25030177 Scientific Series Mathematical physics

DOI10.48660/25030177

Series: Mathematical Physics

Zhang, H. (2025). The sewing-factorization theorem for $C_2$-cofinite VOAs. Perimeter Institute. https://pirsa.org/25030177

Zhang, Hao. The sewing-factorization theorem for $C_2$-cofinite VOAs. Perimeter Institute, Mar. 20, 2025, https://pirsa.org/25030177 

@misc{ pirsa_PIRSA:25030177,
  doi = {10.48660/25030177},
  url = {https://pirsa.org/25030177},
  author = {Zhang, Hao},
  keywords = {Mathematical physics},
  language = {en},
  title = {The sewing-factorization theorem for $C_2$-cofinite VOAs},
  publisher = {Perimeter Institute},
  year = {2025},
  month = {mar},
  note = {PIRSA:25030177 see, \url{https://pirsa.org}}
}

Abstract

In this talk, I will present a sewing-factorization theorem for conformal blocks in arbitrary genus associated to a (possibly nonrational) $C_2$-cofinite VOA $V$. This result gives a higher genus analog of Huang-Lepowsky-Zhang's tensor product theory. Moreover, I will explain the relation between our result and pseudotraces, and confirm some of the conjectures by Gainuditnov-Runkel. The relationship between our result and coends will also be discussed. The talk is based on an ongoing project (arXiv: 2305.10180, 2411.07707) joint with Bin Gui.

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