, Volume 204, Issue 2, pp 439-473

Chiral de Rham Complex

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We define natural sheaves of vertex algebras over smooth manifolds which may be regarded as semi-infinite de Rham complexes of certain D-modules over the loop spaces. For Calabi–Yau manifolds they admit N=2 supersymmetry. Connection with Wakimoto modules is discussed.

Received: 29 April 1998 / Accepted: 7 February 1999