We review the remarkable progress that has been made the last 15 years towards the classification of supersymmetric solutions with emphasis on the description of the bilinears and spinorial geometry methods. We describe in detail the geometry of backgrounds of key supergravity theories, which have applications in the context of black holes, string theory, M-theory and the AdS/CFT correspondence unveiling a plethora of existence and uniqueness theorems. Some other aspects of supersymmetric solutions like the Killing superalgebras and the homogeneity theorem are also presented, and the non-existence theorem for certain smooth supergravity flux compactifications is outlined. Amongst the applications described is the proof of the emergence of conformal symmetry near black hole horizons and the classification of warped AdS backgrounds that preserve more than 16 supersymmetries.

中文翻译：

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超对称背景的分类、几何和应用

我们回顾了过去 15 年来在超对称解分类方面取得的显着进展，重点是对双线性和旋向几何方法的描述。我们详细描述了关键超引力理论背景的几何形状，这些理论在黑洞、弦理论、M 理论和 AdS/CFT 对应关系中都有应用，揭示了大量存在性和唯一性定理。还介绍了超对称解的其他一些方面，如 Killing 超代数和齐次定理，并概述了某些光滑超重力通量紧化的不存在定理。