Abstract
Using exceptional field theory we construct supersymmetric warped AdS7 vacua of massive IIA and AdS6 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 AdS7 vacua with vector multiplets when the Romans mass is non-vanishing. For AdS6 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) × U(1) gauged SUGRA. These consistent truncations with vector multiplets exist when the two holomorphic functions that define the AdS6 vacua satisfy certain differential conditions which we derive. We use these to deduce that no globally regular AdS6 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.
Highlights
Supersymmetric AdS vacua of 10-/11-dimensional SUGRA play an important role in our modern understanding of theoretical physics
We show that there are no consistent truncations of massive IIA supergravity around its supersymmetric AdS7 vacua with vector multiplets when the Romans mass is non-vanishing
And 10 we analyse the possibility of having consistent truncations with matter multiplets around these vacua, using the methods of [29, 30]. It follows that we can have at most three vector multiplets in consistent truncations around supersymmetric AdS7 (AdS6) vacua and, for the truncation to be consistent, the compactification space has to satisfy certain conditions. These extra conditions imply that there are no consistent truncations with vector multiplets around AdS7 vacua for non-vanishing Romans mass
Summary
Supersymmetric AdS vacua of 10-/11-dimensional SUGRA play an important role in our modern understanding of theoretical physics. In a recent paper [51], we showed that in ExFT these infinite families of AdS solutions are described by the same universal generalised half-maximal structure and used this to explain the universal form of the AdS7 consistent truncations and derive the consistent truncation around the AdS6 vacua. It has remained an interesting open problem to find any consistent truncations around the AdS6,7 vacua keeping more modes than just the gravitional supermultiplet.
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