Poisson sigma model on the sphere

TL;DR

This paper evaluates the path integral of the Poisson sigma model on the sphere, establishing conditions for well-definedness, and demonstrates that for holomorphic Poisson structures, semiclassical results are exact quantum correlators.

Contribution

It constructs the finite-dimensional BV theory for the Poisson sigma model and proves semiclassical exactness for holomorphic Poisson structures using localization.

Findings

Path integral well-defined for unimodular Poisson structures

Finite-dimensional BV theory construction

Semiclassical results are exact for holomorphic Poisson structures

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.