AdS_6 solutions of type II supergravity

TL;DR

This work classifies $AdS_6\times M_4$ backgrounds in type II supergravity using the pure spinor formalism, demonstrating that supersymmetry reduces to a pair of PDEs on a two-dimensional base $\Sigma$ with $M_4$ as an $S^2$-fibration over $\Sigma$. The authors construct an explicit $SU(2)_R$-covariant parameterization of the pure spinors $\Phi_\pm$ and $\Psi_\pm$, derive the metric and fluxes in terms of the PDE solution, and analyze both generic and special cases, including a local solution linked to nonabelian T-duality and a no-go result for AdS$_6$ in eleven dimensions. The PDE system is expected to capture near-horizon limits of $p$-$q$ fivebrane webs and thereby provide a framework for new holographic duals to five-dimensional SCFTs. They also firmly establish that no AdS$_6$ solutions exist in eleven-dimensional supergravity and relate the IIB AdS$_6$ backgrounds to known IIA configurations via dualities, offering a robust bridge between brane constructions and geometric classifications.

Abstract

Very few AdS_6 x M_4 supersymmetric solutions are known: one in massive IIA, and two IIB solutions dual to it. The IIA solution is known to be unique; in this paper, we use the pure spinor approach to give a classification for IIB supergravity. We reduce the problem to two PDEs on a two-dimensional space Sigma. M_4 is then a fibration of S^2 over Sigma; the metric and fluxes are completely determined in terms of the solution to the PDEs. The results seem likely to accommodate near-horizon limits of (p,q)-fivebrane webs studied in the literature as a source of CFT_5's. We also show that there are no AdS_6 solutions in eleven-dimensional supergravity.