Kaluza-Klein spectrometry beyond consistent truncations

We show how to use Exceptional Field Theory to compute the full Kaluza-Klein spectra of 10- and 11-dimensional supergravity around deformations of backgrounds of maximal gauged supergravity by scalar modes that do not form part of the consistent truncation. This includes deformations of AdS4 × S7 and AdS5 × S5 by modes that are not part of the N = 8 supermultiplet. As an application, we compute the full Kaluza-Klein spectrum of the N = 1 and N = 0 squashed S7. In this example, all conformal dimensions are captured by a universal formula in terms of the Casimir operators and additional quantum numbers which organise the spectrum.