Symplectic singularities, introduced by Beauville, appear in various aspects of representation theory. Additionally, symplectic singularities arise in the context of quantum field theory, particularly in the Higgs and Coulomb branches of three-dimensional theories, as well as in the Higgs branches of four-dimensional theories. Furthermore, the 4D/2D duality proposed by Beem et al. identifies vertex algebras as invariants for superconformal four-dimensional theories. It has been suggested that the Higgs branch of four-dimensional theories can be reconstructed as the associated variety of vertex algebras. As a result, all vertex algebras arising from four-dimensional theories are believed to be chiral quantizations of symplectic singularities. In this lecture, we will discuss such vertex algebras and their representation theory.
Tomoyuki Arakawa (Research Institute for Mathematical Sciences, Kyoto University)
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Symplectic singularities, introduced by Beauville, appear in various aspects of representation theory. Additionally, symplectic singularities arise in the context of quantum field theory, particularly in the Higgs and Coulomb branches of three-dimensional theories, as well as in the Higgs branches of four-dimensional theories. Furthermore, the 4D/2D duality proposed by Beem et al. identifies vertex algebras as invariants for superconformal four-dimensional theories. It has been suggested that the Higgs branch of four-dimensional theories can be reconstructed as the associated variety of vertex algebras. As a result, all vertex algebras arising from four-dimensional theories are believed to be chiral quantizations of symplectic singularities. In this lecture, we will discuss such vertex algebras and their representation theory.
