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arXiv 0705.2208hep-th
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IIB背景,具有五种形式的通量

IIB backgrounds with five-form flux

U. Gran, J. Gutowski, G. Papadopoulos

摘要:

我们研究了所有N=2超对称IIB超引力背景,具有非零的五种形式的通量。Killing旋量具有稳定子群$Spin(7)\ltimes\bR^8$、$SU(4)\ltimes\bR^8$和$G_2$。在$SU(4)\ltimes\bR^8$的情况下,两种不同类型的几何出现取决于是否是通用的或纯的Killing旋量。在这两种情况下,背景承认零Killing矢量场,这使得$SU(4)\ltimes \bR^8$结构不变,并且在光锥的横向方向上几乎是复杂的结构。在一般情况下,向量场的扭曲是平凡的,但几乎复结构是不可积的,而在纯的情况下,扭曲是非平凡的,但几乎复结构是可积的,并与相对平衡的厄米结构相关联。$G_2$背景允许一个类时基灵向量场和两个类空闭一形式,并且横向于这些的七个方向允许一个共辛$G_2$结构。$Spin(7)\ltimes\bR^8$背景是在具有完整性$Spin(7)$的八维流形中传播的pp波。此外,我们还证明了含类时Killing矢量场的简单五维超引力系统(包括$AdS_5$黑洞)的所有超对称解都提升到$SU(4)\ltimes\bR^8$纯Killing旋量IIB背景.我们还证明了LLM解与一个具有主轨道$S^3\times S^3$的余辛余齐性$G_2$流形有关。

英文摘要:

We investigate all N=2 supersymmetric IIB supergravity backgrounds with non-vanishing five-form flux. The Killing spinors have stability subgroups $Spin(7)\ltimes\bR^8$, $SU(4)\ltimes\bR^8$ and $G_2$. In the $SU(4)\ltimes\bR^8$ case, two different types of geometry arise depending on whether the Killing spinors are generic or pure. In both cases, the backgrounds admit a null Killing vector field which leaves invariant the $SU(4)\ltimes \bR^8$ structure, and an almost complex structure in the directions transverse to the lightcone. In the generic case, the twist of the vector field is trivial but the almost complex structure is non-integrable, while in the pure case the twist is non-trivial but the almost complex structure is integrable and associated with a relatively balanced Hermitian structure. The $G_2$ backgrounds admit a time-like Killing vector field and two spacelike closed one-forms, and the seven directions transverse to these admit a co-symplectic $G_2$ structure. The $Spin(7)\ltimes\bR^8$ backgrounds are pp-waves propagating in an eight-dimensional manifold with holonomy $Spin(7)$. In addition we show that all the supersymmetric solutions of simple five-dimensional supergravity with a time-like Killing vector field, which include the $AdS_5$ black holes, lift to $SU(4)\ltimes\bR^8$ pure Killing spinor IIB backgrounds. We also show that the LLM solution is associated with a co-symplectic co-homogeneity one $G_2$ manifold which has principal orbit $S^3\times S^3$.

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