Supersymmetric spectroscopy on AdS4× S7 and AdS4× S6.

New techniques based on Exceptional Field Theory have recently allowed for the calculation of the Kaluza-Klein spectra of certain AdS₄ solutions of D = 11 and massive IIA supergravity. These are the solutions that consistently uplift on S⁷ and S⁶ from vacua of maximal four-dimensional supergravity with SO(8) and ISO(7) gaugings. In this paper, we provide an algorithmic procedure to compute the complete Kaluza-Klein spectrum of five such AdS₄ solutions, all of them N = 1, and give the first few Kaluza-Klein levels. These solutions preserve SO(3) and U(1) × U(1) internal symmetry in D = 11, and U(1) (two of them) and no continuous symmetry in type IIA. Together with previously discussed cases, our results exhaust the Kaluza-Klein spectra of known supersymmetric AdS₄ solutions in D = 11 and type IIA in the relevant class. [ABSTRACT FROM AUTHOR]