双曲轨道的分层纤维丛、Quinn同调和膜稳定性
Stratified Fiber Bundles, Quinn Homology and Brane Stability of Hyperbolic Orbifolds
摘要：
我们使用同伦理论和K-同调的方法重新讨论了涉及双曲轨道的弦真空的稳定性问题。我们提出了一个定义的第二类弦论在这样的背景下，进一步进行分层系统的纤维束，概括了更传统的orbifold和对称弦的背景，连同一个分类的包装膜由一个合适的广义同调理论。对于双曲orbifolds上的分层纤维空间，我们使用其基本群的代数K-理论和Quinn同调导出膜稳定性的Atiyah-Hirzebruch型谱序列及其提升到K-同调的准则。在这种情况下，稳定的D-膜携带分层电荷，从而在相应的K-同调群上产生新的加法结构。我们将这些考虑扩展到支持H-通量的背景，在那里我们使用基本群的扭群代数的K-群来分析具有K-顺从等距群的局部对称空间的稳定性，并推导出包裹Eilenberg-MacLane谱函子纤维的膜的稳定性条件。
英文摘要：
We revisit the problem of stability of string vacua involving hyperbolic orbifolds using methods from homotopy theory and K-homology. We propose a definition of Type II string theory on such backgrounds that further carry stratified systems of fiber bundles, which generalise the more conventional orbifold and symmetric string backgrounds, together with a classification of wrapped branes by a suitable generalized homology theory. For spaces stratified fibered over hyperbolic orbifolds we use the algebraic K-theory of their fundamental groups and Quinn homology to derive criteria for brane stability in terms of an Atiyah-Hirzebruch type spectral sequence with its lift to K-homology. Stable D-branes in this setting carry stratified charges which induce new additive structures on the corresponding K-homology groups. We extend these considerations to backgrounds which support H-flux, where we use K-groups of twisted group algebras of the fundamental groups to analyse stability of locally symmetric spaces with K-amenable isometry groups, and derive stability conditions for branes wrapping the fibers of an Eilenberg-MacLane spectrum functor.
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