Path integral quantization of the Poisson-Sigma model

TL;DR

This paper applies the Batalin-Vilkovisky antifield quantization method to the Poisson-Sigma model, deriving the partition function for 2D Yang-Mills theory in the case of linear Poisson structures.

Contribution

It introduces a general gauge quantization approach for the Poisson-Sigma model and connects it to known gauge theories like 2D Yang-Mills.

Findings

Derived the path integral for the Poisson-Sigma model in a general gauge.

Obtained the partition function for 2D Yang-Mills theory on closed surfaces.

Extended the antifield quantization method to a broad class of models.

Abstract

We apply the antifield quantization method of Batalin and Vilkovisky to the calculation of the path integral for the Poisson-Sigma model in a general gauge. For a linear Poisson structure the model reduces to a nonabelian gauge theory, and we obtain the formula for the partition function of two-dimensional Yang-Mills theory for closed two-dimensional manifolds.