Comments on higher-spin holography

TL;DR

The work argues for a strong AdS/CFT-like duality between Vasiliev higher-spin gravity in $AdS_{d+1}$ and a boundary vector model of massless scalars with quartic interactions, valid at the Gaussian fixed point for arbitrary $N$ and coupling due to unbroken higher-spin symmetry. It develops the boundary/bulk dictionary through the free CFT, its single-trace and double-trace deformations, and the Flato–Fronsdal theorem, establishing a representation-theoretic mapping between boundary currents $J^{ab}_{\mu_1\cdots\mu_s}$ and bulk higher-spin fields of spin $s$. The analysis shows how double-trace deformations correspond to quadratic boundary terms that modify bulk boundary conditions for a dual scalar, yielding an exact dual description at large $N$ and all couplings, with the Hubbard–Stratonovich approach clarifying the mechanism. The paper also discusses holographic degeneracy across dimensions, linking different boundary conditions to distinct fixed points and RG flows, and thereby connecting boundary operator spectra, bulk gauge fields, and RG dynamics in vector models. Overall, it highlights the potential for a tractable, symmetry-protected derivation of higher-spin AdS/CFT dualities beyond the large-$N$ limit.

Abstract

The conjectured holographic duality between vector models with quartic interaction and higher-spin field theory in the bulk is reviewed, with emphasis on some versions and generalisations (higher dimensions, beyond the singlet sector, etc) which have not been much investigated yet. The strongest form of the conjecture assumes that it holds for any (not necessarily large) number of massless scalar fields and for any value of the coupling constant. Since the quartic interaction is of double-trace type, the exact duality (for any value of the coupling constant) automatically follows from its validity at the Gaussian fixed point (for vanishing coupling constant). The validity of the latter also implies that unbroken higher spin symmetries should prevent quantum corrections in the bulk.