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All AdS7 solutions of type II supergravity

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In M-theory, the only AdS7 supersymmetric solutions are
AdS7 × S4 and its orbifolds. In this talk, I will describe a classification of
AdS7 supersymmetric solutions 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. The classification starts from a pure spinor approach reminiscent of
generalized complex geometry. Without the need for any Ansatz, the method
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. One can obtain numerically many solutions, with D8 and/or D6 brane
sources; topologically, the internal manifold M3 = S^3.