AdS6 solutions of type II supergravity

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 CFT5's. We also show that there are no AdS(6) solutions in eleven-dimensional supergravity.