Classification, geometry and applications of supersymmetric backgrounds

TL;DR

This paper reviews 15 years of progress in classifying supersymmetric backgrounds in supergravity, focusing on geometric methods, key theorems, and applications in black holes, string theory, and AdS/CFT.

Contribution

It provides a comprehensive overview of the classification techniques, geometric analysis, and key theorems related to supersymmetric solutions in supergravity theories.

Findings

Classification of supersymmetric solutions using bilinears and spinorial geometry.

Proof of conformal symmetry emergence near black hole horizons.

Classification of warped AdS backgrounds with high supersymmetry.

Abstract

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.