Gauging the Poisson sigma model

TL;DR

This paper develops a new gauged version of the Poisson sigma model using AKSZ formalism, explores its cohomology, and connects it to topological gauge theories and vortex moduli spaces.

Contribution

It introduces the Poisson--Weil sigma model, extending the Poisson sigma model with a novel gauging approach inspired by AKSZ and Weil models.

Findings

Derived the BV cohomology of the model and related it to Poisson cohomology.

Performed gauge fixing leading to topological gauge theories and vortex moduli space descriptions.

Connected the gauged model to known topological theories like Donaldson--Witten and A-models.

Abstract

We show how to carry out the gauging of the Poisson sigma model in an AKSZ inspired formulation by coupling it to the a generalization of the Weil model worked out in ref. arXiv:0706.1289 [hep-th]. We call the resulting gauged field theory, Poisson--Weil sigma model. We study the BV cohomology of the model and show its relation to Hamiltonian basic and equivariant Poisson cohomology. As an application, we carry out the gauge fixing of the pure Weil model and of the Poisson--Weil model. In the first case, we obtain the 2--dimensional version of Donaldson--Witten topological gauge theory, describing the moduli space of flat connections on a closed surface. In the second case, we recover the gauged A topological sigma model worked out by Baptista describing the moduli space of solutions of the so--called vortex equations.