Triality and the consistent reductions on AdS ₃ × S ³

We 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, 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 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.