arXiv 0907.16652009-07-10hep-th

广义定标与M2-Brane背景的表征

Generalized Calibrations & the Characterization of M2-Brane Backgrounds

Tasneem Zehra Husain

备注：: 19 pages

摘要：

作为一个步骤的超重力背景与通量的分类，我们研究（反反应）的几何形状创建的BPS M2膜时，它包装一个循环的卡-丘流形。如果要保持超对称性，膜背景必须服从一定的条件。这些条件表示为微分形式的几何约束，因此可以解释为校准。知道完整的校准集就等于满足了超对称性保持所需的所有条件。虽然一个纯粹的几何背景是完全指定通过标准校准，为了充分描述通量背景，我们还必须说明其广义校准。这些可以通过用BPS膜探测背景来发现。逻辑很简单。由于BPS探头保证是稳定的，我们要求其体积由校准形式给出。这同样适用于带电和不带电的探针;前者通过通量来稳定，而后者通过最小化它们的体积来实现稳定。带电探针的体积形式对应于广义校准，不带电探针的体积形式对应于标准校准。以前的几何结构只能用不带电的膜来探测。然后，为了保证在通量背景下保持超对称性，必须用额外的条件来补充所发现的校准。一旦范围扩大到包括带电膜，“缺失条件”（广义校准）也可以使用探针分析恢复。我们使用这种方法来分类的包装M2-膜嵌入卡-丘流形的背景，通过指定其校准。

英文摘要：

As a step towards the classification of supergravity backgrounds with flux, we study the (back-reacted) geometry created by a BPS M2-brane when it wraps a cycle in a Calabi-Yau manifold. If it is to preserve supersymmetry, the membrane background must obey certain conditions. These conditions are expressed as geometrical constraints on differential forms and as such, can be interpreted as calibrations. Knowing the complete set of calibrations is the same as satisfying all conditions needed for supersymmetry preservation. While a purely geometric background is completely specified through standard calibrations, in order to fully describe a flux background, we must also state its generalized calibrations. These can be found by probing the background with BPS branes. The logic is simple. Since a BPS probe is guaranteed to be stable, we require that its volume be given by a calibrated form. This applies equally to both charged and uncharged probes; the former are stabilized by flux whereas the latter achieve stability by minimizing their volumes. Volume-forms of charged probes correspond to generalized calibrations and those of uncharged probes, to standard calibrations. Previously geometries were probed only by uncharged branes. The calibrations that were found had then to be supplemented by additional conditions in order to guarantee supersymmetry preservation in backgrounds with flux. Once the scope is broadened to include charged branes, the 'missing conditions' (generalized calibrations) can also be recovered using the probe analysis. We use this method to classify the backgrounds of wrapped M2-branes embedded in Calabi-Yau manifolds by specifying their calibrations.

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