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Six-dimensional chiral gauged Einstein-Maxwell supergravity admits a two-parameter rotating dyonic string solution whose near horizon limit is the direct product of three-dimensional Anti-De Sitter space and a squashed three-sphere $S^3$. For a particular relation between the two parameters, the solution preserves $1/2$supersymmetry. We determine the complete Kaluza-Klein spectrum of the theory around these ${\mathrm{AdS}}_3$backgrounds. For the supersymmetric backgrounds, the states organize into infinite towers of long and short multiplets of $\mathrm{OSp}\left(2\right|2)$. In a certain limit of parameters, both the supersymmetric and the nonsupersymmetric spectra exhibit scale separation. In the latter case there are five topologically massive vectors and five scalars retaining finite masses with integer conformal dimensions, and in the supersymmetric case there are supersymmetric partners with half integer conformal dimensions, while all other masses diverge. Published by the American Physical Society2025 

Abstract We considerN = 1 supergravity coupled to a Wess–Zumino multiplet with a potential such that the resulting AdS energies saturate the unitarity and Breitenlohner–Freedman bounds, respectively. Imposing regular boundary conditions that preserve supersymmetry and support finite norms, the spectrum forms an $OSp(1,4)$supermultiplet in which the singleton representation is absent. We study the case in which this boundary condition is relaxed such that the singleton and its superpartners survive and form an indecomposable representation of $OSp(1,4)$. Focusing on the global limit of the model, we carry out its holographic renormalization, in which a singletonic action makes appearance in the boundary action. Contribution to Stanley Deser memorial volume ‘Gravity, Strings and Beyond’ 

A<sc>bstract</sc> We discuss known maximalD-dimensional supergravities of two types: type I withG/Hcoset spaces and type II derived by compactification from higher dimensions without dualization, these have less manifest symmetries. In 4Dand 6Din type I models we perform explicit gauge-fixing of localHsymmetries in unitary gauges: symmetric, Iwasawa and partial Iwasawa. In 4Dsupergravity I in symmetric gauge globalH-invariance and nonlinearly realizedG-symmetry are valid on shell, classically. The globalH-symmetry andG-symmetry in Iwasawa-type gauges in type I and in type II supergravities are not manifest, if at all present. This fact raises the issue of the gauge equivalence of the S-matrix of various gauge-fixedD-dimensional supergravities and its relation to the ones computable using superamplitude methods.