Chiral Differential Operators on the Basic Affine Space

Although vertex algebras originated in 2D conformal field theory, recent developments show that they also arise in 3D and 4D quantum field theories. Such vertex algebras often appear as chiralizations of symplectic singularities.

To construct new examples of these chiralizations, we study chiral differential operators on the basic affine space G/U, where G is a simple, simply connected algebraic group of type ADE, and U is a maximal unipotent subgroup of G. We show that the associated variety of these vertex algebras is isomorphic to the affine closure of G/U, which is a symplectic singularity, as conjectured by Ginzburg and Kazhdan and later proved by Jia and Gannon.

This is a joint work in progress with Xuanzhong Dai and Bailin Song.