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.
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机译：我们完成了对Poisson-Lie组的Poisson-Sigma模型的研究，首先，我们解决了目标$ G $和$ G ^ * $（Poisson-Lie组$ G $的对偶组）对应于三角形的模型$ r $ -matrix并显示$ G ^ * $之上的模型始终等同于BF理论。然后，给定任意的$ r $矩阵，我们解决了寻找保留模型之间的对偶性的D形问题的问题。我们识别出一类广泛的双脑，它们是$ G $和$ G ^ * $的子组，但不一定是Poisson-Lie子组。特别是，它们在一般情况下不是同向性子流形，更重要的是，我们证明了通过对偶转换，人们可以从同向性金属到非同向性金属。这个事实清楚地表明，非同向性谱是Poisson-Sigma模型的自然边界条件。
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