(Weak) G2 holonomy from self-duality, flux and supersymmetry
(Weak) G2 holonomy from self-duality, flux and supersymmetry
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（弱）来自自对偶性、通量和超对称性的 G2 完整性
DOI：
10.1016/s0550-3213(02)00042-1
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发表时间：
2001
期刊：
影响因子：
--
通讯作者：
K. Sfetsos
中科院分区：
文献类型：
--
作者：
A. Bilal;J. Derendinger;K. Sfetsos
这篇论文的目的有两个。首先，我们提供了一个简单而有教育意义的讨论，即保持某些四维超对称性的M理论或超重力的紧致化如何自然地导致简化的完整或其推广，简化的弱完整。我们将(共形)杀戮旋量的存在与某些封闭的和共封闭的p-形式的存在联系起来，并将度规与Ricci Flat或Einstein联系起来。然后，对于七维流形，我们证明了自旋连接上的八元自对偶条件等价于G2完整，某些广义自对偶条件等价于弱G2完整。后者提升到同齐性的自对偶条件--一个自旋(7)度量。为了说明这种方法的威力，我们举了几个例子，在这些例子中，自对偶条件大大简化了G2或弱G2度量的推导。
The aim of this paper is two-fold. First, we provide a simple and pedagogical discussion of how compactifications of M-theory or supergravity preserving some four-dimensional supersymmetry naturally lead to reduced holonomy or its generalization, reduced weak holonomy. We relate the existence of a (conformal) Killing spinor to the existence of certain closed and co-closed p-forms, and to the metric being Ricci flat or Einstein. Then, for seven-dimensional manifolds, we show that octonionic self-duality conditions on the spin connection are equivalent to G2holonomy and certain generalized self-duality conditions to weak G2holonomy. The latter lift to self-duality conditions for cohomogeneity-one spin(7) metrics. To illustrate the power of this approach, we present several examples where the self-duality condition largely simplifies the derivation of a G2or weak G2metric.