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We complete the study of the Poisson-Sigma model over Poisson-Lie groups.Firstly, we solve the models with targets $G$ and $G^*$ (the dual group of thePoisson-Lie group $G$) corresponding to a triangular $r$-matrix and show thatthe model over $G^*$ is always equivalent to BF-theory. Then, given anarbitrary $r$-matrix, we address the problem of finding D-branes preserving theduality between the models. We identify a broad class of dual branes which aresubgroups of $G$ and $G^*$, but not necessarily Poisson-Lie subgroups. Inparticular, they are not coisotropic submanifolds in the general case and whatis more, we show that by means of duality transformations one can go fromcoisotropic to non-coisotropic branes. This fact makes clear thatnon-coisotropic branes are natural boundary conditions for the Poisson-Sigmamodel.Comment: 24 pages; JHEP style; Final versio

Dual branes in topological sigma models over Lie groups. BF-theory and non-factorizable Lie bialgebras