The coupling of Poisson sigma models to topological backgrounds

TL;DR

This paper generalizes the coupling of Poisson sigma models to topological backgrounds, analyzing the effects on BRST cohomology, observables, and their geometric interpretation, and explores coupling to topological gravity for potential topological string theory applications.

Contribution

It extends the coupling to topological backgrounds to general Poisson sigma models, modifies BRST transformations, and couples the models to topological gravity, opening avenues for topological string theory.

Findings

Coupling involves a Casimir function on the target manifold.

BRST cohomology is altered by the coupling.

Coupling to topological gravity is achieved, linking to topological string theory.

Abstract

We extend the coupling to the topological backgrounds, recently worked out for the 2-dimensional BF-model, to the most general Poisson sigma models. The coupling involves the choice of a Casimir function on the target manifold and modifies the BRST transformations. This in turn induces a change in the BRST cohomology of the resulting theory. The observables of the coupled theory are analyzed and their geometrical interpretation is given. We finally couple the theory to 2-dimensional topological gravity: this is the first step to study a topological string theory in propagation on a Poisson manifold. As an application, we show that the gauge-fixed vectorial supersymmetry of the Poisson sigma models has a natural explanation in terms of the theory coupled to topological gravity.