AdS5 Backgrounds with 24 Supersymmetries

TL;DR

This work proves a no-go for smooth warped Ad$S_5$ backgrounds preserving exactly 24 supersymmetries: there are no such solutions in 11D supergravity or in (massive) IIA, while any $N=24$ AdS$_5$ background in IIB must be locally AdS$_5\times S^5$. Using a near-horizon Killing spinor framework combined with the homogeneity conjecture and maximum principle arguments, the authors show that internal spaces must force the warp factor to be constant and fluxes to vanish in many cases, leading to contradictions with the field equations unless the geometry reduces to the maximally symmetric background. The results have AdS/CFT implications: strictly ${\cal N}=3$ 4D superconformal theories, if they exist, cannot have smooth gravitational duals with compact internal spaces; any dual would be singular or non-compact. The analysis hinges on explicit KSE structures, spinor bilinears, and the global Hopf/maximum principle assumptions that ensure internal spaces span the tangent bundle via isometries.

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.