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

Abstract

We explore all warped AdS 4 × 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 × CP 3 , and in D = 11 supergravity all such backgrounds are locally isometric to the maximally supersymmetric AdS 4 × S 7 solution.

A uniqueness theorem for warped N > 16 Minkowski backgrounds with fluxes

“…Recently, all warped anti-de-Sitter (AdS) backgrounds with fluxes that preserve N > 16 supersymmetries in d = 11 and d = 10 supergravities have been classified up to a local isometry in [1,2,3]. In this note, we extend this result to include all warped R n−1,1 × w M d−n backgrounds of these theories.…”

A non-existence theorem for N > 16 supersymmetric AdS3 backgrounds

“…For the analysis that follows, we use the description of the geometry of the homogeneous space Sp(2)/(Sp(1) × U(1)) presented in [18], where more details can be found. The metric on the internal space CP 3 × S 2 is…”

“…= ℓ 12 + ℓ 34 andω = ℓ 12 are invariant 2-forms on CP 3 whose properties can be found in [18] and σ = ℓ 78 .…”

“…where a description of Spin(7)/G 2 can be found in [18] whose conventions we follow, a, b > 0 are constants and ℓ 8 is an invariant frame on S 1 , dℓ 8 = 0.…”

“…More recently, it has been demonstrated under the same assumptions on the internal space that there are no smooth AdS 5 backgrounds that preserve 16 < N < 32 [14]; see [15,16,17] for applications to AdS/CFT. It has also been shown in [18] that the only smooth AdS 4 solution with compact without boundary internal space that preserves 16 < N < 32 supersymmetries is locally isometric to the N = 24 IIA solution AdS 4 × CP 3 of [19]. Moreover it has been shown in [20] that there are no smooth AdS 2 backgrounds in 10-and 11-dimensional supergravities with compact without boundary internal space that preserve N > 16 supersymmetries.…”