Poisson Sigma Model on the Sphere

2007/06/30 by Francesco Bonechi, Maxim Zabzine
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Black Holes and Theoretical Physics #Homotopy and Cohomology in Algebraic Topology #hep-th #math.SG

paper · pdf · doi:10.1007/s00220-008-0615-1

published as Commun.Math.Phys.285:1033-1063,2009 · 38 pages

openalex publication_date 2008/10/14 · arxiv created 2009/01/13 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/29

Abstract

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.

Citations

• The partition function of the linear Poisson-sigma model on arbitrary surfaces
• On Deformations of Generalized Complex Structures: the Generalized Calabi-Yau Case
• Quantization of Gauge Systems
• Mirror Manifolds And Topological Field Theory
• Topological sigma-models with H-flux and twisted generalized complex manifolds