Communications in Mathematical Physics

, Volume 204, Issue 2, pp 439–473

Chiral de Rham Complex

  • Fyodor Malikov
  • Vadim Schechtman
  • Arkady Vaintrob

DOI: 10.1007/s002200050653

Cite this article as:
Malikov, F., Schechtman, V. & Vaintrob, A. Comm Math Phys (1999) 204: 439. doi:10.1007/s002200050653


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.

Copyright information

© Springer-Verlag Berlin Heidelberg 1999

Authors and Affiliations

  • Fyodor Malikov
    • 1
  • Vadim Schechtman
    • 3
  • Arkady Vaintrob
    • 4
  1. 1.Max-Planck-Institut für Mathematik, Gottfried-Claren-Straße 26, 53225 Bonn, Germany.¶E-mail: malikov@mpim-bonn.mpg.deDE
  2. 2.Department of Mathematics, University of Southern California, Los Angeles, CA 90089, USA.¶E-mail: fmalikov@mathj.usc.eduUS
  3. 3.Department of Mathematics, University of Glasgow, 15 University Gardens, Glasgow G12 8QW, UK.¶E-mail:
  4. 4.Department of Mathematics, New Mexico State University, Las Cruces, NM 88003-8001, USA.¶E-mail: vaintrob@nmsu.eduUS

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