2D sigma models and differential Poisson algebras

Cesar Arias, Nicolas Boulanger, Per Sundell, Alexander Torres-Gomez

Research output: Contribution to journalArticlepeer-review

4 Citations (Scopus)

Abstract

Abstract: We construct a two-dimensional topological sigma model whose target space is endowed with a Poisson algebra for differential forms. The model consists of an equal number of bosonic and fermionic fields of worldsheet form degrees zero and one. The action is built using exterior products and derivatives, without any reference to a worldsheet metric, and is of the covariant Hamiltonian form. The equations of motion define a universally Cartan integrable system. In addition to gauge symmetries, the model has one rigid nilpotent supersymmetry corresponding to the target space de Rham operator. The rigid and local symmetries of the action, respectively, are equivalent to the Poisson bracket being compatible with the de Rham operator and obeying graded Jacobi identities. We propose that perturbative quantization of the model yields a covariantized differential star product algebra of Kontsevich type. We comment on the resemblance to the topological A model.

Original languageEnglish
Article number95
Pages (from-to)1-18
Number of pages18
JournalJournal of High Energy Physics
Volume2015
Issue number8
DOIs
Publication statusPublished - 1 Aug 2015

Keywords

  • Differential and Algebraic Geometry
  • NonCommutative Geometry
  • Topological Field Theories
  • Topological Strings

ASJC Scopus subject areas

  • Nuclear and High Energy Physics

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