The class $\mathcal{S}$ theory is a class of four-dimensional $\mathcal{N}=2$ super CFT, and a class of the corresponding vertex operator algebras is called the chiral algebras of class $\mathcal{S}$. In connection with this theory, Beem and Nair constructed a symplectic open immersion from the cover of the Kostant–Toda lattice associated to $G$ into the universal centralizer of $G$ for a simple linear algebraic group $G$. They expected that a free field realization of the chiral universal centralizer of $G$ at the critical level will be obtained by the chiralization of this immersion. In this talk, I want to explain the details of this conjecture, and verify that it is true by constructing an embedding from the chiral universal centralizer of $G$ into an appropriate vertex operator algebra at any level.

This seminar is a hybrid meeting.
Zoom Meeting ID: 837 0595 2753
Passcode: 449403