The spinorial geometry of supersymmetric backgrounds
The spinorial geometry of supersymmetric backgrounds
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超对称背景的旋旋几何
DOI：
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发表时间：
2004
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通讯作者：
G. Papadopoulos
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文献类型：
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作者：
J. Gillard;Ulf Gran;G. Papadopoulos
基于旋量的形式描述和超协变导数的Spin（1，10）规范对称性，提出了一种求解11维超引力Killing旋量方程的新方法.本文给出了在N = 2，且其中一个旋量表示具有稳定子群SU（5）的Spin（1，10）的轨道时，背景保持两个超对称的Killing旋量的标准形.我们直接求解了N = 1和某些N = 2、N = 3和N = 4背景下的Killing旋量方程。在N = 2的情况下，我们研究了SU（5）和SU（4）不变的Killing旋量的背景，并计算了相关的时空形式。我们发现，具有SU（5）不变Killing旋量的N = 2背景中存在类时Killing向量，且该向量场轨道的横截空间是具有SU（5）-结构的厄米流形.此外，具有SU（4）不变Killing旋量的N = 2背景允许两个Killing向量，一个类时向量和一个类空向量。横截前者轨道的空间是一个具有SU（4）-结构的几乎厄米流形。类空基灵向量场使几乎复结构保持不变。我们探讨了背景保持两个以上的超对称，N > 2的标准型的Killing旋量。研究了一类具有SU（4）不变旋量的N = 3和N = 4背景.我们发现，在这两种情况下，横向于类时向量场的空间都是一个具有SU（4）-结构的厄米流形，并允许两个全纯Killing向量场。我们还提出了一个应用M-理论的Calabi-Yau紧化与通量的一维。
We propose a new method to solve the Killing spinor equations of 11-dimensional supergravity based on a description of spinors in terms of forms and on the Spin(1, 10) gauge symmetry of the supercovariant derivative. We give the canonical form of Killing spinors for backgrounds preserving two supersymmetries, N = 2, provided that one of the spinors represents the orbit of Spin(1, 10) with stability subgroup SU(5). We directly solve the Killing spinor equations of N = 1 and some N = 2, N = 3 and N = 4 backgrounds. In the N = 2 case, we investigate backgrounds with SU(5) and SU(4) invariant Killing spinors and compute the associated spacetime forms. We find that N = 2 backgrounds with SU(5) invariant Killing spinors admit a timelike Killing vector and that the space transverse to the orbits of this vector field is a Hermitian manifold with an SU(5)-structure. Furthermore, N = 2 backgrounds with SU(4) invariant Killing spinors admit two Killing vectors, one timelike and one spacelike. The space transverse to the orbits of the former is an almost Hermitian manifold with an SU(4)-structure. The spacelike Killing vector field leaves the almost complex structure invariant. We explore the canonical form of Killing spinors for backgrounds preserving more than two supersymmetries, N > 2. We investigate a class of N = 3 and N = 4 backgrounds with SU(4) invariant spinors. We find that in both cases the space transverse to a timelike vector field is a Hermitian manifold equipped with an SU(4)-structure and admits two holomorphic Killing vector fields. We also present an application to M-theory Calabi–Yau compactifications with fluxes to one dimension.