The first Pontryagin class
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.(Received January 10 2006)
(Accepted October 24 2006)
Key Words: Courant algebroid; vertex algebroid; gerbe; chiral differential operators.
14F10 (primary); 57N65 (secondary).