PIRSA:25010072

A new construction of $c=1$ Virasoro conformal blocks

(2025). A new construction of $c=1$ Virasoro conformal blocks. Perimeter Institute. https://pirsa.org/25010072

A new construction of $c=1$ Virasoro conformal blocks. Perimeter Institute, Jan. 07, 2025, https://pirsa.org/25010072 

          @misc{ pirsa_PIRSA:25010072,
            doi = {10.48660/25010072},
            url = {https://pirsa.org/25010072},
            author = {},
            keywords = {Quantum Fields and Strings},
            language = {en},
            title = {A new construction of $c=1$ Virasoro conformal blocks},
            publisher = {Perimeter Institute},
            year = {2025},
            month = {jan},
            note = {PIRSA:25010072 see, \url{https://pirsa.org}}
          }
Qianyu Hao
Talk number
PIRSA:25010072
Collection
Talk Type
Subject
Abstract

The Virasoro conformal blocks are very interesting since they have many connections to other areas of math and physics. For example, when $c=1$, they are related to tau functions of integrable systems of Painlev\'{e} equations. They are also closely related to non-perturbative completions in the topological string theories. I will first explain what Virasoro conformal blocks are. Then I will describe a new way to construct Virasoro blocks at $c=1$ on $C$ by using the "abelian" Heisenberg conformal blocks on a branched double cover of C. The main new idea in our work is to use a spectral network and I will show the advantages of this construction. This nonabelianization construction enables us to compute the harder-to-get Virasoro blocks using the simpler abelian objects. It is closely related to the idea of nonabelianization of the flat connections in the work of Gaiotto-Moore-Neitzke and Neitzke-Hollands. This is based on a joint work with Andrew Neitzke.