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Poisson Sigma Model on the Sphere

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Abstract

We evaluate the path integral of the Poisson sigma model on the sphere and study the correlators of quantum observables. We argue that for the path integral to be well-defined the corresponding Poisson structure should be unimodular. The construction of the finite dimensional BV theory is presented and we argue that it is responsible for the leading semiclassical contribution. For a (twisted) generalized Kähler manifold we discuss the gauge fixed action for the Poisson sigma model. Using the localization we prove that for the holomorphic Poisson structure the semiclassical result for the correlators is indeed the full quantum result.

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Authors and Affiliations

  1. I.N.F.N. and Dipartimento di Fisica, Via G. Sansone 1, 50019, Sesto Fiorentino, Firenze, Italy

    Francesco Bonechi

  2. Department of Theoretical Physics, Uppsala University, Box 803, SE-751 08, Uppsala, Sweden

    Maxim Zabzine

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  1. Francesco Bonechi
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  2. Maxim Zabzine
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Correspondence to Maxim Zabzine.

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Communicated by N.A. Nekrasov

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Bonechi, F., Zabzine, M. Poisson Sigma Model on the Sphere. Commun. Math. Phys. 285, 1033–1063 (2009). https://doi.org/10.1007/s00220-008-0615-1

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