Differential Geometry and Physics Seminar

Speaker: Surya Raghavendran, Yale

Title: Towards a Dolbeault AGT correspondence

Abstract: The AGT correspondence and its extensions propose geometric constructions of vertex algebras and their modules from the cohomology of various moduli spaces of sheaves on surfaces. Physically, the correspondence is illuminated throgh the holomorphic–topological twist of the six-dimensional N=(2,0) superconformal field theories. In this talk, I will describe a variant of AGT arising instead from the so-called minimal twist of these theories. In this setting, the natural algebraic structures are holomorphic factorization algebras in three complex dimensions. From these, one can extract an associative algebra together with a natural module, which we conjecture to coincide with a quantization of the moduli of Higgs sheaves on surfaces. In examples, this pair is furthermore expected to admit a Hodge–de Rham deformation to the Heisenberg algebra and its action on the cohomology of Hilbert schemes of surfaces, as constructed by Grojnowski and Nakajima.