Towards a Dolbeault AGT correspondence

          @misc{ scivideos_PIRSA:25110069,
            doi = {10.48660/25110069},
            url = {https://pirsa.org/25110069},
            author = {Raghavendran, Surya},
            keywords = {Mathematical physics},
            language = {en},
            title = {Towards a Dolbeault AGT correspondence},
            publisher = {Perimeter Institute for Theoretical Physics},
            year = {2025},
            month = {nov},
            note = {PIRSA:25110069 see, \url{https://scivideos.org/pirsa/25110069}}
          }
          

Abstract

The AGT correspondence and its extensions posit geometric constructions of vertex algebras and their modules from cohomology of variants of moduli of sheaves on surfaces. Physically, the correspondence has found an explanation through the holomorphic-topological twist of the six dimensional N=(2,0) superconformal field theories. In this talk, I’ll propose a variant of the AGT correspondence coming from the so-called minimal twist of these theories. Instead of vertex algebras, the natural algebras appearing will be holomorphic factorization algebras in three complex dimensions. From this data, I will explain how one extracts an associative algebra and a module which conjecturally agrees with a quantization of moduli of Higgs sheaves on surfaces. In examples, the pair will admit a Hodge-deRham deformation to the Heisenberg algebra and its action on cohomology of Hilbert schemes of surfaces, constructed in work of Grojnowski-Nakajima.