AdS 6 solutions of type II supergravity

Very few AdS 6 × 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 Σ. M 4 is then a fibration of S 2 over Σ; 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