PIRSA:25030177

The sewing-factorization theorem for $C_2$-cofinite VOAs

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}}
          }

Hao Zhang Tsinghua University

Talk numberPIRSA:25030177
DOI10.48660/25030177
Collection
Talk Type Scientific Series
Subject

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.