We analyse in detail the language of partially non-abelian Deligne cohomology and of twisted differential K-theory, in order to describe the geometry of type II superstring backgrounds with D-branes. This description will also provide the opportunity to show some mathematical results of independent interest. In particular, we begin classifying the possible gauge theories on a D-brane or on a stack of D-branes using the intrinsic tool of long exact sequences. Afterwards, we recall how to construct two relevant models of differential twisted K-theory, paying particular attention to the dependence on the twisting cocycle within its cohomology class. In this way we will be able to define twisted K-homology and twisted Cheeger-Simons K-characters in the category of simply-connected manifolds, eliminating any unnatural dependence on the cocycle. The ambiguity left for non simply-connected manifolds will naturally correspond to the ambiguity in the gauge theory, following the previous classification. This picture will allow for a complete characterization of D-brane world-volumes, the Wess-Zumino action and topological D-brane charges within the K-theoretical framework, that can be compared step by step to the old cohomological classification. This has already been done for backgrounds with vanishing B-field; here we remove this hypothesis.

我们详细分析了部分非阿贝尔的Deligne同调和扭曲的微分K-理论的语言，以描述带有D-brains的II型超弦背景的几何形状。该描述还将提供机会展示一些独立兴趣的数学结果。尤其是，我们开始使用长精确序列的内在工具对D膜片或D膜片堆栈上的可能量规理论进行分类。之后，我们回想起如何构造微分扭曲K理论的两个相关模型，并特别注意其同调性类中对扭曲共轭的依赖性。通过这种方式，我们将能够定义扭曲的K-同调和扭曲的Cheeger-Simons K-在简单连接歧管类别中的字符，从而消除了对cocycle的任何不自然的依赖。按照先前的分类，非简单连接的歧管所留下的歧义自然将对应于规范理论中的歧义。这张图将完整描述D膜世界体积，K理论框架内的Wess-Zumino作用和拓扑D膜电荷，可以将其逐步与旧的同调分类进行比较。对于B场消失的背景，这已经完成；这里我们删除这个假设。