AdS4 backgrounds with N>16 supersymmetries in 10 and 11 dimensions

TL;DR

This paper classifies all warped AdS4 backgrounds with more than 16 supersymmetries in 10 and 11-dimensional supergravity, finding only known maximally supersymmetric solutions and one with 24 supersymmetries.

Contribution

It provides a comprehensive classification of highly supersymmetric AdS4 backgrounds in supergravity, showing the absence of new solutions beyond known maximally supersymmetric ones.

Findings

No such backgrounds in IIB supergravity.

Unique 24-supersymmetry background in IIA supergravity is AdS4×CP3.

All 11D backgrounds are locally isometric to AdS4×S^7.

Abstract

We explore all warped $AdS_4\times_w M^{D-4}$ backgrounds with the most general allowed fluxes that preserve more than 16 supersymmetries in $D=10$- and $11$-dimensional supergravities. After imposing the assumption that either the internal space $M^{D-4}$ is compact without boundary or the isometry algebra of the background decomposes into that of AdS$_4$ and that of $M^{D-4}$, we find that there are no such backgrounds in IIB supergravity. Similarly in IIA supergravity, there is a unique such background with 24 supersymmetries locally isometric to $AdS_4\times \mathbb{CP}^3$, and in $D=11$ supergravity all such backgrounds are locally isometric to the maximally supersymmetric $AdS_4\times S^7$ solution.