环空间上旋子的康恩融合

IF 1.3 1区 数学 Q1 MATHEMATICS Compositio Mathematica Pub Date : 2024-08-27 DOI:10.1112/s0010437x24007188
Peter Kristel, Konrad Waldorf
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引用次数: 0

摘要

弦流形的环空间支持一个无限维的福克空间束,它与自旋流形上的自旋束类似。这个环空间上的旋子束在二维西格玛模型的描述中作为超弦配置空间上的状态束出现。我们在这个束上构建了一个乘积,它涵盖了环的融合,即两个环沿着一个共同的线段合并。为此,我们将其展示为某个冯-诺依曼代数束上的双模束,并利用冯-诺依曼双模的康恩融合实现我们的乘积。我们的主要技术是在弦结构、环融合和福克空间的康恩融合之间建立新的关系。环空间旋量束上的融合乘积是斯托尔兹和泰克纳提出的,作为探索广义同调理论、函子场论和索引理论之间关系的计划的一部分。它与超弦的一对裤子世界表、相应的平滑扇形场论向下到点的扩展,以及底层弦流形上的高分类束--弦束相关。
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Connes fusion of spinors on loop space

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 two-dimensional sigma models as the bundle of states over the configuration space of the superstring. We construct a product on this bundle that covers 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 novel relations 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 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.

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来源期刊
Compositio Mathematica
Compositio Mathematica 数学-数学
CiteScore
2.10
自引率
0.00%
发文量
62
审稿时长
6-12 weeks
期刊介绍: Compositio Mathematica is a prestigious, well-established journal publishing first-class research papers that traditionally focus on the mainstream of pure mathematics. Compositio Mathematica has a broad scope which includes the fields of algebra, number theory, topology, algebraic and differential geometry and global analysis. Papers on other topics are welcome if they are of broad interest. All contributions are required to meet high standards of quality and originality. The Journal has an international editorial board reflected in the journal content.
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