Triality and the consistent reductions on ${\mathrm{AdS}}_3\times S^3$

Abstract

We study compactifications on ${\mathrm{AdS}}_3\times S^3$ and deformations thereof. We exploit the triality symmetry of the underlying duality group $\mathrm{SO}(4,4)$ 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 ${\mathrm{AdS}}_3\times M^3$ backgrounds on squashed spheres preserving $\mathrm{U}(1{)}^2$ 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 ${\mathrm{AdS}}_3\times M^3$ backgrounds on squashed spheres with $\mathrm{U}(2)$ isometries. Using techniques from exceptional field theory, we determine the full Kaluza-Klein spectrum around these backgrounds.

arXiv comment44 pages, 6 figures, v2: accepted in JHEP, matches accepted version

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• Warped compactifications and holographic duality
• $\mathcal{N}=1$ S-fold spectroscopy