Supersymmetric AdS7 and AdS6 vacua and their consistent truncations with vector multiplets

Using exceptional field theory we construct supersymmetric warped AdS(7) vacua of massive IIA and AdS(6) vacua of IIB, as well as their consistent truncations including vector multiplets. We show that there are no consistent truncations of massive IIA supergravity around its supersymmetric AdS(7) vacua with vector multiplets when the Romans mass is non-vanishing. For AdS(6) vacua of IIB supergravity, we find that in addition to the consistent truncation to pure F(4) gauged SUGRA, the only other half-maximal truncations that are consistent result in F(4) gauged SUGRA coupled to one or two Abelian vector multiplets, to three non-Abelian vector multiplets, leading to an ISO(3) gauged SUGRA, or to three non-Abelian plus one Abelian vector multiplet, leading to an ISO(3) x U(1) gauged SUGRA. These consistent truncations with vector multiplets exist when the two holomorphic functions that define the AdS(6) vacua satisfy certain differential conditions which we derive. We use these to deduce that no globally regular AdS(6) solutions admit a consistent truncation to F(4) gauged SUGRA with two vector multiplets, and show that the Abelian T-dual of the Brandhuber-Oz vacuum allows a consistent truncation to F(4) gauged SUGRA with a single vector multiplet.