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arXiv 0810.4291hep-thmath-phmath.MP
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D-膜存在时A-场和B-场构型的分类

Classifying A-field and B-field configurations in the presence of D-branes

Loriano Bonora, Fabio Ferrari Ruffino, Raffaele Savelli

摘要:

我们“求解”Freed-Witten异常方程,即,我们发现在无反常的D-膜的存在下,B-场和A-场配置的几何分类。由格贝斯几何提供的数学设置,我们发现,允许的配置共同描述的陪集的某个超上同调群。然后,我们详细描述了根据这种分类出现的各种情况。众所周知,只有在适当的假设下,A场才是正则规范丛上的联络。然而,即使在这些情况下,在丛的选择中也有剩余的自由,这自然是由超上同调描述引起的。对于一个在D-膜上平坦的B-场,自然会出现子膜的分数或无理荷;对于一个合适的规范选择,它们可以被看作是从“非整陈类的规范丛”中产生的:我们给出了这些对象的精确几何解释。

英文摘要:

We "solve" the Freed-Witten anomaly equation, i.e., we find a geometrical classification of the B-field and A-field configurations in the presence of D-branes that are anomaly-free. The mathematical setting being provided by the geometry of gerbes, we find that the allowed configurations are jointly described by a coset of a certain hypercohomology group. We then describe in detail various cases that arise according to such classification. As is well-known, only under suitable hypotheses the A-field turns out to be a connection on a canonical gauge bundle. However, even in these cases, there is a residual freedom in the choice of the bundle, naturally arising from the hypercohomological description. For a B-field which is flat on a D-brane, fractional or irrational charges of subbranes naturally appear; for a suitable gauge choice, they can be seen as arising from "gauge bundles with not integral Chern class": we give a precise geometric interpretation of these objects.

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。

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