Poisson Sigma Models and String Theory

一般背景场论中的开弦理论在低能有效场论中的D-膜上引入了一个非对易结构。这只在特定的、相当简单的背景下被证明，但据信在更普遍的情况下也是如此。另一方面，预期的非对易几何由孔采维奇公式提供，而孔采维奇公式又由一类非常特殊的（拓扑）弦理论，即所谓的泊松-西格玛模型描述。本文的目的是在任意弯曲弦背景下建立膜非对易几何与某些极限Poisson Sigma模型之间的精确关系。此外，我们想利用这个关系来构造描述一般弯曲背景下膜动力学的非对易规范理论。在这种背景下，提出和研究Poisson sigma模型的新的拓扑推广也将是有趣的，这些推广都是由更一般的弦背景（例如NS或RR通量）以及它们与最近在数学中考虑的Poisson几何的各种推广（例如Dirac结构）的关系所激发的。

Open string theories in generic background fields induce a noncommutative structure on D-branes present in the low energy effective field theories. This is proven only for particular, rather simple backgrounds, but believed to hold much more generally. The expected noncommutative geometries, on the other hand, are provided by the Kontsevich formula which is again described by a very special class of (topological) string theories, namely the so-called Poisson Sigma Models. It is intended to establish the precise relation between brane non-commutative geometry and some limiting Poisson Sigma Model for arbitrary curved string backgrounds. Furthermore, we want to use this relation for constructing the non-commutative gauge theories that describe the dynamics of branes in general curved backgrounds. In this context, it will be also interesting to propose and study new topological generalizations of the Poisson sigma model that are both motivated by more general string backgrounds (e.g. with NS or RR-fluxes) and by their relation with various generalizations of Poisson geometry that have been considered in Mathematics recently (such as e.g. Dirac-structures).