Abelianization of Virasoro blocks at c=1

          @misc{ pirsa_PIRSA:25110047,
            doi = {10.48660/25110047},
            url = {https://pirsa.org/25110047},
            author = {Neitzke, Andrew},
            keywords = {Mathematical physics},
            language = {en},
            title = {Abelianization of Virasoro blocks at c=1},
            publisher = {Perimeter Institute},
            year = {2025},
            month = {nov},
            note = {PIRSA:25110047 see, \url{https://pirsa.org}}
          }
          

Abstract

I will describe a new method for constructing conformal blocks for the Virasoro vertex algebra with central charge c=1, by relating them to conformal blocks for the Heisenberg algebra on a branched double cover. The construction is joint work with Qianyu Hao. It fits into the "holomorphic-topological" theme of the conference only inasmuch as vertex algebras are holomorphic objects and nonabelianization involves topological line defects. One concrete output is new formulas for tau functions in the sense of integrable systems -- most concretely, for Painleve equations -- as I will briefly explain; this part is joint work in progress with Dawit Belayneh and Davide Gaiotto.