Vacua of different gaugings of D = 4 N = 8 supergravity that preserve the same supersymmetries and bosonic symmetry tend to exhibit the same universal mass spectrum within their respective supergravities. For AdS 4 vacua in gauged supergravities that arise upon consistent truncation of string/M-theory, we show that this universality is lost at higher Kaluza-Klein levels. However, universality is still maintained in a milder form, as certain sums over a finite number of states remain universal. Further, we derive a mass matrix for Kaluza-Klein gravitons which is valid for all the AdS 4 vacua in string/M-theory that uplift from the gaugings of D = 4 N = 8 supergravity that we consider. The mild universality of mass sums is related to the trace of this mass matrix.

The SU(3)-invariant sector of maximal supergravity in four dimensions with an SO(8) gauging is uplifted to D = 11 supergravity. In order to do this, the SU(3)-neutral sector of the tensor and duality hierarchies of the D = 4 N = 8 supergravity is first worked out. The consistent D = 11 embedding of the full, dynamical SU(3) sector is then expressed at the level of the D = 11 metric and three-form gauge field in terms of these D = 4 tensors. The redundancies introduced by this approach are eliminated at the level of the D = 11 four-form field strength by making use of the D = 4 duality hierarchy. Our results encompass previously known truncations of D = 11 supergravity down to sectors of SO(8) supergravity with symmetry larger than SU(3), and include new ones. In particular, we obtain a new consistent truncation of D = 11 supergravity to minimal D = 4 N = 2 gauged supergravity. The SU(3)-invariant sector of SO(8) supergravityLet us start by reviewing some aspects of the SU(3) sector of SO(8)-gauged supergravity. We choose a triangular, or Iwasawa, parametrisation for the (SU(3)-invariant truncation of the) E 7(7) /SU(8) coset representative. Since previous literature often chooses the unitary gauge for the coset, we believe that our presentation has some intrinsic value even if the material that is covered (the Lagrangian in section 2.1, the further subsectors in 2.3, and the vacuum structure in 2.4) is mostly review. The SU(3)-invariant, restricted tensor and duality hierarchies worked out in section 2.2 are new.

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.

We present a new consistent truncation of D = 11 supergravity to D = 4 N = 2 minimal gauged supergravity, on the seven-dimensional internal Riemannian space corresponding to the most general class of D = 11 solutions with an AdS 4 factor and N = 2 supersymmetry. A truncation ansatz is proposed and its consistency checked at the level of the D = 11 Bianchi identity, bosonic equations of motion, and supersymmetry variations of the gravitino. The general class includes an N = 2 AdS 4 solution dual to the conformal, low-energy physics phase corresponding to a mass deformation of the M2-brane field theory. A consistent truncation recently constructed on this particular geometry is recovered from our formalism.

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.

We analyse the spectrum of Kaluza-Klein excitations above three distinct families of $$ \mathcal{N} $$ N = 1 AdS4 solutions of type IIB supergravity of typically non-geometric, S-fold type that have been recently found. For all three families, we provide the complete algebraic structure of their spectra, including the content of OSp(4|1) multiplets at all Kaluza-Klein levels and their charges under the residual symmetry groups. We also provide extensive results for the multiplet dimensions using new methods derived from exceptional field theory, including complete, analytic results for one of the families. All three spectra show periodicity in the moduli that label the corresponding family of solutions. Finally, the compactness of these moduli is verified in some cases at the level of the fully-fledged type IIB uplifted solutions.

We study compactifications on AdS3×S3 and deformations thereof. We exploit the triality symmetry of the underlying duality group SO(4,4) of three-dimensional supergravity in order to construct and relate new consistent truncations. For non-chiral D = 6, $$ \mathcal{N} $$ N 6d = (1, 1) supergravity, we find two different consistent truncations to three-dimensional supergravity, retaining different subsets of Kaluza-Klein modes, thereby offering access to different subsectors of the full nonlinear dynamics. As an application, we construct a two-parameter family of AdS3 × M3 backgrounds on squashed spheres preserving U(1)2 isometries. For generic value of the parameters, these solutions break all supersymmetries, yet they remain perturbatively stable within a non-vanishing region in parameter space. They also contain a one-parameter family of $$ \mathcal{N} $$ N = (0, 4) supersymmetric AdS3 × M3 backgrounds on squashed spheres with U(2) isometries. Using techniques from exceptional field theory, we determine the full Kaluza-Klein spectrum around these backgrounds.