Sheaves of N=2 supersymmetric vertex algebras on Poisson manifolds

Joel Ekstrand*, Reimundo Heluani, Maxim Zabzine

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

We construct a sheaf of N=2 vertex algebras naturally associated to any Poisson manifold. The relation of this sheaf to the chiral de Rham complex is discussed. We reprove the result about the existence of two commuting N=2 superconformal structures on the space of sections of the chiral de Rham complex of a Calabi-Yau manifold, but now calculated in a manifest N=2 formalism. We discuss how the semi-classical limit of this sheaf of N=2 vertex algebras is related to the classical supersymmetric non-linear sigma model.

Original languageEnglish (US)
Pages (from-to)2259-2278
Number of pages20
JournalJournal of Geometry and Physics
Volume62
Issue number11
DOIs
StatePublished - Nov 2012

Keywords

  • Poisson geometry
  • Poisson vertex algebra
  • SUSY vertex algebra
  • Vertex algebra

ASJC Scopus subject areas

  • Mathematical Physics
  • Physics and Astronomy(all)
  • Geometry and Topology

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