Triality and the consistent reductions on AdS3 × S3
Camille Eloy, Gabriel Larios, Henning Samtleben
Abstract
A bstract 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, $$ \mathcal{N} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>N</mml:mi> </mml:math> 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 $$ \mathcal{N} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>N</mml:mi> </mml:math> = (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.