Consistent massive truncations of type-IIB supergravity on Sasaki-Einstein manifolds

Recent work on holographic superconductivity and gravitational duals of systems with nonrelativistic conformal symmetry have made use of consistent truncations of $D=10$ and $D=11$ supergravity retaining some massive modes in the Kaluza-Klein tower. In this paper we focus on reductions of type-IIB supergravity to five dimensions on a Sasaki-Einstein manifold, and extend these previous truncations to encompass the entire bosonic sector of gauged $D=5$, N=2 supergravity coupled to massive multiplets up to the second Kaluza-Klein level. We conjecture that a necessary condition for the consistency of massive truncations is to only retain the lowest modes in the massive trajectories of the Kaluza-Klein mode decomposition of the original fields. This is an extension of the well-known result that consistent truncations may be obtained by restricting to the singlet sector of the internal symmetry group.