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arXiv 1010.5789hep-th
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多维中的广义几何、校准与超对称性

Generalized geometry, calibrations and supersymmetry in diverse dimensions

Dieter Lust, Peter Patalong, Dimitrios Tsimpis

备注：
28 pages, 1 table
发表信息：
JHEP 1101:063,2011
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摘要：

我们考虑第二类背景的形式为R^{1，d-1} x M^{10-d}（d为偶数），保留2^{d/2}个实超荷;当d = 4，6，8时，这是d维的最小超对称，而当d = 2时，这是二维的N =（2，0）超对称。对于d = 6，我们证明，通过显式求解Killing-spinor方程，在纯旋量形式的背景超对称方程和D-膜广义校准之间存在一一对应;这种对应在d = 4的情况下是已知的。假设对应关系对所有d都成立，我们列出了所有可容许的D-膜的校准形式，以及纯旋量形式的背景超对称方程。我们发现了一些一般的功能，包括以下内容：在每个校准形式出现的余维的图案表现出（mod 4）的周期性。在所有情况下，其中一个纯旋量方程意味着内部流形是广义卡-丘流形。我们的结果在广义镜像对称下是明显不变的。

英文摘要：

We consider type II backgrounds of the form R^{1,d-1} x M^{10-d} for even d, preserving 2^{d/2} real supercharges; for d = 4, 6, 8 this is minimal supersymmetry in d dimensions, while for d = 2 it is N = (2,0) supersymmetry in two dimensions. For d = 6 we prove, by explicitly solving the Killing-spinor equations, that there is a one-to-one correspondence between background supersymmetry equations in pure-spinor form and D-brane generalized calibrations; this correspondence had been known to hold in the d = 4 case. Assuming the correspondence to hold for all d, we list the calibration forms for all admissible D-branes, as well as the background supersymmetry equations in pure-spinor form. We find a number of general features, including the following: The pattern of codimensions at which each calibration form appears exhibits a (mod 4) periodicity. In all cases one of the pure-spinor equations implies that the internal manifold is generalized Calabi-Yau. Our results are manifestly invariant under generalized mirror symmetry.

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