Geometry of all supersymmetric type I backgrounds
Geometry of all supersymmetric type I backgrounds
复制标题
所有超对称 I 型背景的几何形状
DOI：
10.1088/1126-6708/2007/08/074
复制
发表时间：
2007
影响因子：
5.4
通讯作者：
P. Sloane
中科院分区：
文献类型：
--
作者：
Ulf Gran;G. Papadopoulos;D. Roest;P. Sloane
在所有情况下，我们使用旋量几何技术，通过求解引力和扩张杀旋量方程，找到所有超对称 I 型背景的几何形状。 gravitino Killing 旋量方程的解由它们在 Spin(9,1) 中的各向同性群来表征，而 dilatino Killing 旋量方程的解则由它们在 Spin(9,1) 的子群 Sigma(P) 中的各向同性群来表征，该子群保留了平行旋量 P 的空间。给定具有 L 个平行旋量的 gravitino Killing 旋量方程的解，L = 1,2,3,4,5,6,8， dilatino Killing 旋量方程允许对于任何 0 < N =< L 具有 N 个超对称性的解。此外，对于 L = 16，我们确认 N = 8,10,12,14,16。我们发现，在大多数情况下，I 类背景的比安奇恒等式和场方程意味着超协变连接的完整性的进一步降低。此外，我们还表明，在某些情况下，如果超协变连接的完整群恰好是平行旋量的各向同性群，则所有平行旋量都是 Killing，因此不存在 N < L 超对称性的背景。
We find the geometry of all supersymmetric type I backgrounds by solving the gravitino and dilatino Killing spinor equations, using the spinorial geometry technique, in all cases. The solutions of the gravitino Killing spinor equation are characterized by their isotropy group in Spin(9,1), while the solutions of the dilatino Killing spinor equation are characterized by their isotropy group in the subgroup Sigma(P) of Spin(9,1) which preserves the space of parallel spinors P. Given a solution of the gravitino Killing spinor equation with L parallel spinors, L = 1,2,3,4,5,6,8, the dilatino Killing spinor equation allows for solutions with N supersymmetries for any 0 < N =< L. Moreover for L = 16, we confirm that N = 8,10,12,14,16. We find that in most cases the Bianchi identities and the field equations of type I backgrounds imply a further reduction of the holonomy of the supercovariant connection. In addition, we show that in some cases if the holonomy group of the supercovariant connection is precisely the isotropy group of the parallel spinors, then all parallel spinors are Killing and so there are no backgrounds with N < L supersymmetries.