论文标题
$ n \ geq 5 $ in $ d = 11 $ supergravity supersmmetric $ ds_n $ solutions for $ n \ geq 5 $
Supersymmetric $dS_n$ solutions for $n \geq 5$ in $D=11$ supergravity
论文作者
论文摘要
我们确定扭曲产品的必要条件$ ds_n $ solutions，$ 5 \ leq n \ leq 10 $，以将超对称性保存在$ d = 11 $的超级重力中，而无需假设杀戮旋转器的分解。我们证明，$ 7 \ leq n \ leq 10 $，所有此类解决方案都是平坦的，其消失了4型。我们还表明，唯一扭曲的产品$ ds_6 $ solutions是最大的超级对称$ ads_7 \ times s^4 $解决方案，或$ \ mathbb {r}^{1,6} \ times n_4 $，其中$ n_4 $ n_4 $是Hyperkahler，是Hyperkahler，具有消失的4型。然后对超对称扭曲的产品$ DS_5 $解决方案进行分类；结果表明，所有此类解决方案都是通用的M5-Brane配置，横向空间为$ \ Mathbb {r} \ times n_4 $，而$ n_4 $是HyperKahler歧管。如果4形式是协变量的，则$ n_4 $承认Hyperkahler潜力。
We determine the necessary and sufficient conditions for warped product $dS_n$ solutions, $5 \leq n \leq 10$, to preserve supersymmetry in $D=11$ supergravity, without assuming factorization of the Killing spinors. We prove that for $7 \leq n \leq 10$, all such solutions are flat, with vanishing 4-form. We also show that the only warped product $dS_6$ solutions are either the maximally supersymmetric $AdS_7 \times S^4$ solution, or $\mathbb{R}^{1,6} \times N_4$ where $N_4$ is hyperKahler, with vanishing 4-form. Supersymmetric warped product $dS_5$ solutions are then classified; it is shown that all such solutions are generalized M5-brane configurations, for which the transverse space is $\mathbb{R} \times N_4$, and $N_4$ is a hyperKahler manifold. If the 4-form is covariantly constant, then $N_4$ admits a hyperKahler potential.
