Poisson sigma model on the sphere

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.

38 pages

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• Twistor Strings for N=8 Supergravity
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• 2D sigma models and differential Poisson algebras
• Finite dimensional AKSZ-BV theories
• Generalized Calabi-Yau manifolds and the chiral de Rham complex
• Gauging the Poisson sigma model
• Equivariant Batalin-Vilkovisky formalism
• Comparing Poisson Sigma Model with A-model
• Superconformal structures on generalized Calabi-Yau metric manifolds
• The gauging of BV algebras
• AKSZ construction from reduction data
• Basic curvature and the Atiyah cocycle in gauge theory
• Boundary coupling of Lie algebroid Poisson sigma models and representations up to homotopy
• Observables in the equivariant A-model
• The coupling of Poisson sigma models to topological backgrounds
• Instances of Higher Geometry in Field Theory
• Computation of Kontsevich Weights of Connection and Curvature Graphs for Symplectic Poisson Structures
• A topological quantum field theory for $\mathrm{Spin}(7)$-instantons