We provide a systematic approach to describing the Ramond–Ramond (RR) fields as elements in twisted differential K-theory. This builds on a series of constructions by the authors on geometric and computational aspects of twisted differential K-theory, which to a large extent were originally motivated by this problem. In addition to providing a new conceptual framework and a mathematically solid setting, this allows us to uncover interesting and novel effects. Explicitly, we use our recently constructed Atiyah–Hirzebruch spectral sequence (AHSS) for twisted differential K-theory to characterize the RR fields and their quantization, which involves interesting interplay between geometric and topological data. We illustrate this with the examples of spheres, tori, and Calabi-Yau threefolds.

中文翻译：

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Ramond-Ramond 场和扭曲微分 K 理论

我们提供了一种系统的方法来将 Ramond-Ramond (RR) 场描述为扭曲微分 K 理论中的元素。这建立在作者对扭曲微分 K 理论的几何和计算方面的一系列构造之上，这些构造在很大程度上最初是由这个问题引起的。除了提供新的概念框架和数学上可靠的设置外，这还使我们能够发现有趣和新颖的效果。明确地说，我们使用我们最近构建的 Atiyah-Hirzebruch 谱序列 (AHSS) 进行扭曲微分 K 理论来表征 RR 场及其量化，这涉及几何和拓扑数据之间有趣的相互作用。我们用球体、圆环和卡拉比-丘三重体的例子来说明这一点。