  In this paper, we construct various simple vertex superalgebras which are
extensions of affine vertex algebras, by using abelian cocycle twists of
representation categories of quantum groups. This solves the Creutzig and
Gaiotto conjectures in the case of type ABC. If the twist is trivial, the
resulting algebras correspond to chiral differential operators in the chiral
case, and to WZW models in the non-chiral case.
