2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/162343We 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.25 pagesQuantum AlgebraMathematical Physicstext