Supersymmetry of the chiral de Rham complex

David Ben-Zvi*, Reimundo Heluani, Matthew Szczesny

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

25 Scopus citations


We present a superfield formulation of the chiral deRham complex (CDR), as introduced by Malikov, Schechtman and Vaintrob in 1999, in the setting of a general smooth manifold, and use it to endow CDR with superconformal structures of geometric origin. Given a Riemannian metric, we construct an N=1 structure on CDR (action of the N=1 super-Virasoro, or NeveuSchwarz, algebra). If the metric is Khler, and the manifold Ricci-flat, this is augmented to an N=2 structure. Finally, if the manifold is hyperkhler, we obtain an N=4 structure. The superconformal structures are constructed directly from the Levi-Civita connection. These structures provide an analog for CDR of the extended supersymmetries of nonlinear -models.

Original languageEnglish (US)
Pages (from-to)503-521
Number of pages19
JournalCompositio Mathematica
Issue number2
StatePublished - Mar 2008


  • Chiral de Rham
  • Hyperkähler

ASJC Scopus subject areas

  • Algebra and Number Theory


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