论文标题
Conne旋转旋转空间上的旋转器融合
Connes fusion of spinors on loop space
论文作者
论文摘要
字符串歧管的循环空间支持无限尺寸的Fock空间束，这是旋转歧管上旋转束的类似物。循环空间上的旋转捆绑包在二维Sigma模型的描述中，作为在超音线的配置空间上的状态束。我们在此捆绑包上构造一个产品，涵盖了环的融合，即沿公共段的两个环合并。为此，我们将其显示为在某个von Neumann代数束上的一束双模模，并使用von Neumann Bimodules的融合来实现我们的产品纤维。我们的主要技术是建立弦结构，环融合和Fock空间融合之间的新颖关系。 Stolz和Teichner在旋转空间上的旋转束束上的融合产物是计划的一部分，以探讨广义的共同体理论，功能性领域理论和索引理论之间的关系。它与SuperString的一对裤子世界表相关，与相应的平滑功能场理论的扩展到点，以及在下面的字符串歧管上的较高分类捆绑包，“弹簧串”束。
The loop space of a string manifold supports an infinite-dimensional Fock space bundle, which is an analog of the spinor bundle on a spin manifold. This spinor bundle on loop space appears in the description of 2-dimensional sigma models as the bundle of states over the configuration space of the superstring. We construct a product on this bundle covering the fusion of loops, i.e., the merging of two loops along a common segment. For this purpose, we exhibit it as a bundle of bimodules over a certain von Neumann algebra bundle, and realize our product fibrewise using the Connes fusion of von Neumann bimodules. Our main technique is to establish a novel relation between string structures, loop fusion, and the Connes fusion of Fock spaces. The fusion product on the spinor bundle on loop space was proposed by Stolz and Teichner as a part of a programme to explore the relation between generalized cohomology theories, functorial field theories, and index theory. It is related to the pair of pants worldsheet of the superstring, to the extension of the corresponding smooth functorial field theory down to the point, and to a higher-categorical bundle on the underlying string manifold, the stringor bundle.
