Symmetries of Holographic Super-Minimal Models

TL;DR

This paper computes the asymptotic symmetry algebra of higher-spin supergravity in AdS_3, identifies it as super-W_infinity[lambda], and provides evidence for a duality with a boundary N=2 Kazama-Suzuki model by matching algebraic structures and spectra.

Contribution

It explicitly derives the super-W_infinity[lambda] algebra from supergravity and confirms the duality by matching algebraic relations and spectra with the boundary CFT.

Findings

The super-W_infinity[lambda] algebra is obtained from supergravity.

The algebra matches the chiral algebra of the dual CFT in the 't Hooft limit.

Spectra of chiral primary fields are identical on both sides.

Abstract

We compute the asymptotic symmetry of the higher-spin supergravity theory in AdS_3 and obtain an infinite-dimensional non-linear superalgebra, which we call the super-W_infinity[lambda] algebra. According to the recently proposed supersymmetric duality between higher-spin supergravity in an AdS_3 background and the 't Hooft limit of the N=2 CP^n Kazama-Suzuki model on the boundary, this symmetry algebra should agree with the 't Hooft limit of the chiral algebra of the CFT, SW_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_infinity[lambda] 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 the spectra of the chiral primary fields are identical.