PIRSA:25010072

Video URL

https://pirsa.org/25010072

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

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

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

          @misc{ scivideos_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 for Theoretical Physics},
            year = {2025},
            month = {jan},
            note = {PIRSA:25010072 see, \url{https://scivideos.org/pirsa/25010072}}
          }
Qianyu Hao
Talk numberPIRSA:25010072
DOI10.48660/25010072
Source RepositoryPIRSA
Collection
Talk Type Scientific Series
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.