Using Exceptional Field Theory, we determine the infinite-dimensional mass matrices for the gravitino and spin-1/2 Kaluza-Klein perturbations above a class of anti-de Sitter solutions of M-theory and massive type IIA string theory with topologically-spherical internal spaces. We then use these mass matrices to compute the spectrum of Kaluza-Klein fermions about some solutions in this class with internal symmetry groups containing SU(3). Combining these results with previously known bosonic sectors of the spectra, we give the complete spectrum about some $$ \mathcal{N} $$ N = 1 and some non-supersymmetric solutions in this class. The complete spectra are shown to enjoy certain generic features.

A holographic duality was recently established between an $$ \mathcal{N} $$ N = 4 non-geometric AdS4 solution of type IIB supergravity in the so-called S-fold class, and a three- dimensional conformal field theory (CFT) defined as a limit of $$ \mathcal{N} $$ N = 4 super-Yang-Mills at an interface. Using gauged supergravity, the $$ \mathcal{N} $$ N = 2 conformal manifold (CM) of this CFT has been assessed to be two-dimensional. Here, we holographically characterise the large-N operator spectrum of the marginally-deformed CFT. We do this by, firstly, providing the algebraic structure of the complete Kaluza-Klein (KK) spectrum on the associated two-parameter family of AdS4 solutions. And, secondly, by computing the $$ \mathcal{N} $$ N = 2 super-multiplet dimensions at the first few KK levels on a lattice in the CM, using new exceptional field theory techniques. Our KK analysis also allows us to establish that, at least at large N, this $$ \mathcal{N} $$ N = 2 CM is topologically a non-compact cylindrical Riemann surface bounded on only one side.

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 $$ \mathcal{N} $$ 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.

A superpotential deformation that is cubic in one of the chiral superfields of ABJM makes the latter theory flow into a new $$ \mathcal{N} $$ N = 2 superconformal phase. This is holographically dual to a warped AdS4×wS7 solution of M-theory equipped with a squashed and stretched metric on S7. We determine the spectrum of spin-2 operators of the cubic deformation at low energies by computing the spectrum of Kaluza-Klein (KK) gravitons over the dual AdS4 solution. We calculate, numerically, the complete graviton spectrum and, analytically, the spectrum of gravitons that belong to short multiplets. We also use group theory to assess the structure of the full KK spectrum, and conclude that $$ \mathcal{N} $$ N = 2 supermultiplets cannot be allocated KK level by KK level. This phenomenon, usually referred to as “space invaders scenario”, is also known to occur for another AdS4 solution based on a different squashed S7.