Non-linear sigma models via the chiral de Rham complex

Joel Ekstrand, Reimundo Heluani, Johan Källén, Maxim Zabzine*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

12 Scopus citations


We propose a physical interpretation of the chiral de Rham complex as a formal Hamiltonian quantization of the supersymmetric non-linear sigma model. We show that the chiral de Rham complex on a Calabi-Yau manifold carries all information about the classical dynamics of the sigma model. Physically, this provides an operator realization of the non-linear sigma model. Mathematically, the idea suggests the use of Hamiltonian flow equations within the vertex algebra formalism with the possibility to incorporate both left and right moving sectors within one mathematical framework.

Original languageEnglish (US)
Pages (from-to)1221-1254
Number of pages34
JournalAdvances in Theoretical and Mathematical Physics
Issue number4
StatePublished - Aug 2009

ASJC Scopus subject areas

  • Mathematics(all)
  • Physics and Astronomy(all)


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