The Poisson sigma model on closed surfaces

  • Francesco Bonechi
  • Alberto S. CattaneoEmail author
  • Pavel Mnev


Using methods of formal geometry, the Poisson sigma model on a closed surface is studied in perturbation theory. The effective action, as a function on vacua, is shown to have no quantum corrections if the surface is a torus or if the Poisson structure is regular and unimodular (e.g., symplectic). In the case of a Kähler structure or of a trivial Poisson structure, the partition function on the torus is shown to be the Euler characteristic of the target; some evidence is given for this to happen more generally. The methods of formal geometry introduced in this paper might be applicable to other sigma models, at least of the AKSZ type.


Topological Field Theories Field Theories in Lower Dimensions Sigma Models 


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Copyright information

© SISSA, Trieste, Italy 2012

Authors and Affiliations

  • Francesco Bonechi
    • 1
  • Alberto S. Cattaneo
    • 2
    Email author
  • Pavel Mnev
    • 2
  1. 1.INFN.and Dipartimento di FisicaSesto FiorentinoItaly
  2. 2.Institut für MathematikUniversität ZürichZürichSwitzerland

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