Universal Kaluza–Klein reductions of type IIB to N = 4 supergravity in five dimensions

We construct explicit consistent Kaluza–Klein reductions of type IIB supergravity on HK4 × S, where HK4 is an arbitrary four-dimensional hyper-Kähler manifold, and on SE5, an arbitrary five-dimensional Sasaki– Einstein manifold. In the former case we obtain the bosonic action of D = 5 N = 4 (ungauged) supergravity coupled to two vector multiplets. For the SE5 case we extend a known reduction, which leads to minimal D = 5 N = 2 gauged supergravity, to also include a multiplet of massive fields, containing the breathing mode of the SE5. We show that the resulting D = 5 action is also consistent with N = 4 gauged supergravity coupled to two vector multiplets. This theory has a supersymmetric AdS5 vacuum, which uplifts to the class of supersymmetric AdS5 × SE5 solutions, that spontaneously breaks N = 4 to N = 2, and also a nonsupersymmetric AdS5 vacuum which uplifts to a class of solutions first found by Romans.