Geometry of Killing spinors in neutral signature
Geometry of Killing spinors in neutral signature
复制标题
中性签名中消旋旋量的几何
DOI：
10.1088/0264-9381/32/18/185012
复制
发表时间：
2015
影响因子：
3.5
通讯作者：
Masato Nozawa
中科院分区：
文献类型：
--
作者：
D. Klemm;Masato Nozawa
我们对四维最小N = 2规范超引力的超对称解进行了分类。它们是根据宇宙学常数的符号和是否作为一个双线性的Killing旋量构造的向量场是零或非零的区别。在中性签名中，双线性向量场可以是类空的，这是洛伦兹签名中没有的新特征。在Λ < 0？>在非空的情况下，度量的标准形由具有U（1）？>带挠的完整性我们发现一个广义的killing方程决定了双线性Killing场的扭曲，这让人想起爱因斯坦-外尔结构。此外，如果电磁场强度是自对偶的，我们就得到了普扎诺夫斯基-托德类度规的克莱因签名模拟，即由连续户田方程的解确定的伪厄米时空，它共形于标量平坦的伪凯勒流形，并且还允许一个带电的共形基灵旋量。在Λ < 0？>零的情况下，超对称解定义了一个可积的零Kähler结构。在Λ > 0？>在非零的情况下，该流形是洛伦兹高杜雄-托德基空间上的纤维化。最后，在Λ > 0？>空类，度量包含在Kundt族中，结果证明完整性简化为Sim（1）× Sim（1）？> .对于宇宙常数的任何一个符号，在空类中都没有自对偶解。
We classify the supersymmetric solutions of minimal N = 2 gauged supergravity in four dimensions with neutral signature. They are distinguished according to the sign of the cosmological constant and whether the vector field constructed as a bilinear of the Killing spinor is null or non-null. In neutral signature the bilinear vector field can be spacelike, which is a new feature not arising in Lorentzian signature. In the Λ < 0 ?> non-null case, the canonical form of the metric is described by a fibration over a three-dimensional base space that has U ( 1 ) ?> holonomy with torsion. We find that a generalized monopole equation determines the twist of the bilinear Killing field, which is reminiscent of an Einstein–Weyl structure. If, moreover, the electromagnetic field strength is self-dual, one gets the Kleinian signature analogue of the Przanowski–Tod class of metrics, namely a pseudo-hermitian spacetime determined by solutions of the continuous Toda equation, conformal to a scalar-flat pseudo-Kähler manifold, and admitting in addition a charged conformal Killing spinor. In the Λ < 0 ?> null case, the supersymmetric solutions define an integrable null Kähler structure. In the Λ > 0 ?> non-null case, the manifold is a fibration over a Lorentzian Gauduchon–Tod base space. Finally, in the Λ > 0 ?> null class, the metric is contained in the Kundt family, and it turns out that the holonomy is reduced to Sim ( 1 ) × Sim ( 1 ) ?> . There appear no self-dual solutions in the null class for either sign of the cosmological constant.
影响因子：
2.8
作者：
Martelli D
通讯作者：
Martelli D
宇宙学爱因斯坦-麦克斯韦瞬子和欧几里德超对称性：超越自对偶性
影响因子：
5.4
作者：
Dunajski M
通讯作者：
Dunajski M