arXivDaily arXiv每日学术速递 周一至周五更新
arXiv周末暂无论文更新,休息一下吧,周末愉快~~
arXiv 1104.2798hep-thmath-phmath.MP
收藏

D-膜存在时A-场和B-场构形的分类.第II部分:D-膜的叠层

Classifying A-field and B-field configurations in the presence of D-branes - Part II: Stacks of D-branes

Fabio Ferrari Ruffino

摘要:

在论文arXiv:0810.4291中,我们在II型超弦理论的背景下,给出了在无反常D-膜存在的情况下,B-场和A-场配置的分类,数学框架由格贝斯几何提供。在这里,我们详细考虑了一堆D-膜的情况,完成了讨论,它带有一个非阿贝尔规范理论,这在前一篇论文中刚刚概述过。在这种情况下,我们必须将描述B场的阿贝尔格贝几何与更高秩的普通或扭曲丛几何混合起来。我们详细描述了根据这样一种分类而出现的各种情况,就像我们对单个D-膜所做的那样,说明了在哪些假设下A-场是正则规范丛上的一个联络。我们还将“非整陈类规范丛”的讨论推广到非阿贝尔情形,并将其与具有联络的扭丛联系起来。最后,我们分析了D-膜或D-膜堆上每种规范理论的威尔逊圈的几何性质。

英文摘要:

In the paper arXiv:0810.4291 we have shown, in the context of type II superstring theory, the classification of the allowed B-field and A-field configurations in the presence of anomaly-free D-branes, the mathematical framework being provided by the geometry of gerbes. Here we complete the discussion considering in detail the case of a stack of D-branes, carrying a non-abelian gauge theory, which was just sketched in the previous paper. In this case we have to mix the geometry of abelian gerbes, describing the B-field, with the one of higher-rank bundles, ordinary or twisted. We describe in detail the various cases that arise according to such a classification, as we did for a single D-brane, showing under which hypoteses the A-field turns out to be a connection on a canonical gauge bundle. We also generalize to the non-abelian setting the discussion about "gauge bundles with non integral Chern classes", relating them to twisted bundles with connection. Finally, we analyze the geometrical nature of the Wilson loop for each kind of gauge theory on a D-brane or stack of D-branes.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

↑