Item

Abstract

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 there are no consistent
truncations of massive IIA supergravity around its supersymmetric AdS$_7$ vacua
with vector multiplets when the Roman's mass is non-vanishing. For AdS$_6$
vacua of IIB supergravity, we find that in addition to the consistent
truncation to pure $\mathrm{F}(4)$ gauged SUGRA, the only other half-maximal
truncations that are consistent result in $\mathrm{F}(4)$ gauged SUGRA coupled
to one or two Abelian vector multiplets, to three non-Abelian vector
multiplets, leading to an $\mathrm{ISO}(3)$ gauged SUGRA, or to three
non-Abelian plus one Abelian vector multiplet, leading to an $\mathrm{ISO}(3)
\times \mathrm{U}(1)$ 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 $\mathrm{F}(4)$ gauged SUGRA with two vector multiplets, and show that the
Abelian T-dual of the Brandhuber-Oz vacuum allows a consistent truncation to
$\mathrm{F}(4)$ gauged SUGRA with a single vector multiplet.