W-algebras and chiral differential operators at the critical level

Let Acrit be the chiral algebra corresponding to the affine Kac–Moody algebra at the critical level . Let Zcrit be the center of Acrit. The commutative chiral algebra Zcrit admits a canonical deformation into a non-commutative chiral algebra Wℏ. In this paper we will express the resulting first order deformation via the chiral algebra Dcrit of chiral differential operators on G((t)) at the critical level.