Consistent supersymmetric Kaluza-Klein truncations with massive modes

We construct consistent Kaluza-Klein reductions of D = 11 supergravity to four dimensions using an arbitrary seven-dimensional Sasaki-Einstein manifold. At the level of bosonic fields, we extend the known reduction, which leads to minimal N = 2 gauged supergravity, to also include a multiplet of massive fields, containing the breathing mode of the Sasaki-Einstein space, and still consistent with N = 2 supersymmetry. In the context of flux compactifications, the Sasaki-Einstein reductions are generalizations of type IIA SU(3)-structure reductions which include both metric and form-field flux and lead to a massive universal tensor multiplet. We carry out a similar analysis for an arbitrary weak G 2 manifold leading to an N = 1 supergravity with massive fields. The straightforward extension of our results to the case of the seven-sphere would imply that there is a four-dimensional Lagrangian with N = 8 supersymmetry containing both massless and massive spin two fields. We use our results to construct solutions of M-theory with non-relativistic conformal symmetry.