Coisotropic submanifolds in Poisson geometry and branes in the Poisson sigma model
Coisotropic submanifolds in Poisson geometry and branes in the Poisson sigma model
复制标题
DOI：
10.1007/s11005-004-0609-7
复制
发表时间：
2003-09
影响因子：
1.2
通讯作者：
A. Cattaneo;G. Felder
中科院分区：
文献类型：
--
作者：
A. Cattaneo;G. Felder
研究了Poisson sigma模型的一般边界条件（膜）.他们原来是标记的余迷向子流形的泊松流形。这些边界条件在经典和微扰量子水平所发挥的作用进行了讨论。它原来是相关的经典水平的范畴泊松流形与对偶对作为态射和微扰量子水平的范畴结合代数（变形代数的功能泊松流形）与双模作为态射。可能奇异泊松流形所产生的减少自然进入图片，特别是，建设收益率（在某些假设下）其变形量化。
General boundary conditions (‘branes’) for the Poisson sigma model are studied. They turn out to be labeled by coisotropic submanifolds of the given Poisson manifold. The role played by these boundary conditions both at the classical and at the perturbative quantum level is discussed. It turns out to be related at the classical level to the category of Poisson manifolds with dual pairs as morphisms and at the perturbative quantum level to the category of associative algebras (deforming algebras of functions on Poisson manifolds) with bimodules as morphisms. Possibly singular Poisson manifolds arising from reduction enter naturally into the picture and, in particular, the construction yields (under certain assumptions) their deformation quantization.