Poisson sigma model over group manifolds

TL;DR

This paper explores the Poisson sigma model on group manifolds with Poisson-Lie structures, analyzing boundary conditions, D-branes, and the moduli space of solutions, revealing their relation to coisotropic subgroups and duality properties.

Contribution

It provides a detailed study of D-branes and classical solution moduli space in the Poisson sigma model over group manifolds with Poisson-Lie structures, highlighting their classification and duality features.

Findings

D-branes are labeled by coisotropic subgroups of G

Moduli space of solutions characterized for surfaces with boundaries

Comments on duality properties of the model

Abstract

We study the Poisson sigma model which can be viewed as a topological string theory. Mainly we concentrate our attention on the Poisson sigma model over a group manifold G with a Poisson-Lie structure. In this case the flat connection conditions arise naturally. The boundary conditions (D-branes) are studied in this model. It turns out that the D-branes are labelled by the coisotropic subgroups of G. We give a description of the moduli space of classical solutions over Riemann surfaces both without and with boundaries. Finally we comment briefly on the duality properties of the model.