Poisson sigma model on the sphere

Details Poisson sigma model on the sphere Poisson sigma model on the sphere

2007-06-21

arxiv.org/abs/0706.3164v3

Commun.Math.Phys.285:1033-1063,2009

Physics

High Energy Physics

High Energy Physics - Theory

38 pages

Scientific paper

10.1007/s00220-008-0615-1

We evaluate the path integral of the Poisson sigma model on 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 Kahler 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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