arXiv 0812.06822008-12-03hep-thmath.KT

K-理论、D-膜和Ramond-Ramond场

K-Theory, D-Branes and Ramond-Ramond Fields

Alessandro Valentino

备注：: Ph.D. Thesis, 220 pages, 1 figure

摘要：

本论文致力于研究D-膜和Ramond-Ramond场的K-理论性质。构造了定义CW-复形范畴上的同调理论的交换群，证明了该同调理论等价于KO-同调的协边表示，等价于KO-同调的对偶理论.我们构造了我们的几何表示和KO-同调的解析表示之间的同构，从而导出了同调函子的自然等价性。我们应用这个框架来描述第一类弦论中D-膜的数学性质。本文研究了定义在整体轨道上的第二类弦论中Ramond-Ramond场的规范理论。利用Bredon上同调机制和等变Chern特征标构造阿贝尔群，将Hopkins和Singer定义的微分K-理论的性质推广到等变情形，可以认为是有限群等变K-理论的微分推广.证明了良轨道上Ramond-Ramond场强的Dirac量子化条件是由等变K-理论和等变Chern特征决定的，并利用轨道微分K-理论研究了线性轨道上的平坦Ramond-Ramond场群.

英文摘要：

This thesis is dedicated to the study of K-theoretical properties of D-branes and Ramond-Ramond fields. We construct abelian groups which define a homology theory on the category of CW-complexes, and prove that this homology theory is equivalent to the bordism representation of KO-homology, the dual theory to KO-theory. We construct an isomorphism between our geometric representation and the analytic representation of KO-homology, which induces a natural equivalence of homology functors. We apply this framework to describe mathematical properties of D-branes in type I String theory. We investigate the gauge theory of Ramond-Ramond fields arising from type II String theory defined on global orbifolds. We use the machinery of Bredon cohomology and the equivariant Chern character to construct abelian groups which generalize the properties of differential K-theory defined by Hopkins and Singer to the equivariant setting, and can be considered as a differential extension of equivariant K-theory for finite groups. We show that the Dirac quantization condition for Ramond-Ramond fieldstrengths on a good orbifold is dictated by equivariant K-theory and the equivariant Chern character, and study the group of flat Ramond-Ramond fields in the particular case of linear orbifolds in terms of our orbifold differential K-theory.

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英文摘要：

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