AdS5 Backgrounds with 24 Supersymmetries

TL;DR

This paper proves that smooth, compact, boundaryless AdS5 backgrounds with exactly 24 supersymmetries do not exist in supergravity theories, implying constraints on possible duals of certain superconformal theories.

Contribution

It establishes a non-existence theorem for such backgrounds in D=11, IIB, and (massive) IIA supergravity under specific conditions, clarifying the landscape of supersymmetric AdS5 solutions.

Findings

No smooth AdS5 solutions with 24 supersymmetries in D=11 supergravity.

All IIB solutions with 24 supersymmetries are locally isometric to AdS_5 x S^5.

Such solutions do not exist in (massive) IIA supergravity under the homogeneity conjecture.

Abstract

We prove a non-existence theorem for smooth AdS5 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 strictly N=3 superconformal theories in 4-dimensions exist, their gravitational dual backgrounds are either singular or their internal spaces are not compact.