Symmetries of holographic super-minimal models

A bstractWe compute the asymptotic symmetry of the higher-spin supergravity theory in AdS3 and obtain an infinite-dimensional non-linear superalgebra, which we call the super-W∞[λ] algebra. According to the recently proposed supersymmetric duality between higher-spin supergravity in an AdS3 background and the ’t Hooft limit of the $ \mathcal{N}=2 $$ \mathbb{C}{{\mathrm{P}}^n} $ Kazama-Suzuki model on the boundary, this symmetry algebra should agree with the ’t Hooft limit of the chiral algebra of the CFT, $ \mathcal{S}{{\mathcal{W}}_n} $. We provide two nontrivial checks of the duality. By comparing the algebras, we explicitly match the lowest-spin commutation relations in the super-W∞[λ] with the corresponding commutation relations in the ’t Hooft limit on the CFT side. We also consider the degenerate representations of the two algebras and find that any degenerate representation of the $ \mathbb{C}{{\mathrm{P}}^n} $ model can be a representation of the super-W∞[λ] algebra and vice versa.