The first Pontryagin class

Abstract

We give a natural obstruction theoretic interpretation to the first Pontryagin class in terms of Courant algebroids. As an application we calculate the class of the stack of algebras of chiral differential operators. In particular, we establish the existence and uniqueness of the chiral de Rham complex.

The present paper supercedes the earlier notes ``Vertex algebroids I and II combining their contents and correcting the errors