Algebras of twisted chiral differential operators and affine localization of $\mathfrak{g}$-modules

Tomoyuki Arakawa, Dmytro Chebotarov, Fyodor Malikov

We propose a notion of algebra of {\it twisted} chiral differential operators over algebraic manifolds with vanishing 1st Pontrjagin class. We show that such algebras possess famil…