AdS5 backgrounds with 24 supersymmetries

Abstract

We prove a non-existence theorem for smooth AdS 5 solutions with connected, compact without boundary internal space that preserve strictly 24 supersymmetries. In particular, we show that D = 11 supergravity does not admit such solutions, and that all such solutions of IIB supergravity are locally isometric to the AdS 5 × S 5 maximally supersymmetric background. Furthermore, we prove that (massive) IIA supergravity also does not admit such solutions, provided that the homogeneity conjecture for massive IIA supergravity is valid. In the context of AdS/CFT these results imply that if gravitational duals for strictly N = 3 superconformal theories in 4-dimensions exist, they are either singular or their internal spaces are not compact.

All superalgebras for warped AdS 2 and black hole near horizon geometries

“…Furthermore we demonstrated that there are no near horizon geometries and AdS 2 backgrounds that preserve N > 16 supersymmetries in 10-and 11-dimensional supergravity theories under the same assumptions as those utilized to prove the horizon conjecture. This together with the results of [25], [27] and [28] classify all the warped AdS n backgrounds, for n = 2, 4, 5 in 10-and 11-dimensional supergravity theories that preserve N > 16 supersymmetries up to at most discrete identifications. Product solutions AdS n × M D−n with M D−n symmetric space, D = 10, 11, have been classified in [29]- [32].…”

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

“…As the Bianchi identities require that dZ = 0, we have β = 0. Furthermore the remaining Bianchi identities imply 14) and the field equations for the fluxes give…”

“…There are no AdS 7 backgrounds that preserve 16 < N < 32 supersymmetries [10,11,12] and no smooth AdS 6 backgrounds that preserve N > 16 supersymmetries with compact without boundary internal space [13]. 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].…”