Triality and the consistent reductions on AdS$_{3}$ × S$^{3}$

International audienceWe study compactifications on AdS$_{3}$×S$^{3}$ 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} _{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 AdS$_{3}$ × M$^{3}$ 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} $ = (0, 4) supersymmetric AdS$_{3}$ × M$^{3}$ backgrounds on squashed spheres with U(2) isometries. Using techniques from exceptional field theory, we determine the full Kaluza-Klein spectrum around these backgrounds