Holography of the N=1 Higher-Spin Theory on AdS4

TL;DR

This paper establishes and analyzes a holographic duality between the ${\cal N}=1$ higher-spin theory on AdS$_4$ (built from two singleton sectors and organized into ${\rm Osp}(1|4)$ supermultiplets) and the ${\cal N}=1$ supersymmetric $O(N)$ vector model in three dimensions. By carefully choosing boundary conditions for the bulk scalars and spinors, the authors realize two large-$N$ boundary fixed points: a free theory and a strongly coupled interacting theory, which are related by a Legendre (double-trace) transform and distinguished by parity assignments. They show how bulk boundary conditions translate into boundary deformations (mass terms, marginal double-trace deformations, and SUSY-breaking deformations) and discuss how subleading-$N$ corrections Higgs the higher-spin gauge symmetry in the interacting case, producing anomalous dimensions for the boundary currents. The results illuminate how both fixed points coexist within a single bulk theory and how the interplay of regular and irregular modes encodes UV/IR data, with implications for SUSY, parity, and the fate of higher-spin symmetries at finite $N$.

Abstract

We argue that the N=1 higher-spin theory on AdS4 is holographically dual to the N=1 supersymmetric critical O(N) vector model in three dimensions. This appears to be a special form of the AdS/CFT correspondence in which both regular and irregular bulk modes have similar roles and their interplay leads simultaneously to both the free and the interacting phases of the boundary theory. We study various boundary conditions that correspond to boundary deformations connecting, for large-N, the free and interacting boundary theories. We point out the importance of parity in this holography and elucidate the Higgs mechanism responsible for the breaking of higher-spin symmetry for subleading N.