Supersymmetry of the chiral de Rham complex II: Commuting Sectors
  We construct two commuting N=2 structures on the space of sections of the chiral de Rham complex (CDR) of a Calabi-Yau manifold. We use this extra supersymmetry to construct a non-linear automorphism of CDR preserving these N=2 structures. Finally, we show how to extend these results to construct a commuting pair of N=4 super-vertex algebras in the Hyper-Kahler case. 
Reimundo Heluani