All AdS₇ solutions of type II supergravity

In M-theory, the only AdS₇ supersymmetric solutions are AdS₇×S⁴ and its orbifolds. In this paper, we find and classify new supersymmetric solutions of the type AdS₇×M₃ in type II supergravity. While in IIB none exist, in IIA with Romans mass (which does not lift to M-theory) there are many new ones. We use a pure spinor approach reminiscent of generalized complex geometry. Without the need for any Ansatz, the system determines uniquely the form of the metric and fluxes, up to solving a system of ODEs. Namely, the metric on M₃ is that of an S² fibered over an interval; this is consistent with the Sp(1) R-symmetry of the holographically dual (1,0) theory. By including D8 brane sources, one can numerically obtain regular solutions, where topologically M₃≅S³