On the AdS Higher Spin / O(N) Vector Model Correspondence: degeneracy of the holographic image

TL;DR

This paper investigates the duality between the critical O(N) vector model and higher spin theory in AdS, analyzing four-point functions, fusion coefficients, and the effects of IR flow and degeneracy in the holographic image.

Contribution

It analytically establishes the structure of boundary correlators and their bulk duals, including the factorization of fusion coefficients and the impact of degeneracy on the holographic correspondence.

Findings

Explicitly computed four-point functions and fusion coefficients.

Confirmed the extremal nature of the three-point scalar bilinear correlator in d=3.

Extended previous results from d=3 to general dimensions 2<d<4.

Abstract

We explore the conjectured duality between the critical O(N) vector model and minimal bosonic massless higher spin (HS) theory in AdS. In the boundary free theory, the conformal partial wave expansion (CPWE) of the four-point function of the scalar singlet bilinear is reorganized to make it explicitly crossing-symmetric and closed in the singlet sector, dual to the bulk HS gauge fields. We are able to analytically establish the factorized form of the fusion coefficients as well as the two-point function coefficient of the HS currents. We insist in directly computing the free correlators from bulk graphs with the unconventional branch. The three-point function of the scalar bilinear turns out to be an "extremal" one at d=3. The four-leg bulk exchange graph can be precisely related to the CPWs of the boundary dual scalar and its shadow. The flow in the IR by Legendre transforming at leading 1/N, following the pattern of double-trace deformations, and the assumption of degeneracy of the hologram lead to the CPWE of the scalar four-point function at IR. Here we confirm some previous results, obtained from more involved computations of skeleton graphs, as well as extend some of them from d=3 to generic dimension 2<d<4.