On the AdS higher spin / O(N) vector model correspondence: degeneracy of the holographic image

We explore the conjectured duality between the critical O(N) vector model andminimal bosonic massless higher spin (HS) theory in AdS. In the boundary freetheory, the conformal partial wave expansion (CPWE) of the four-point functionof the scalar singlet bilinear is reorganized to make it explicitlycrossing-symmetric and closed in the singlet sector, dual to the bulk HS gaugefields. We are able to analytically establish the factorized form of the fusioncoefficients as well as the two-point function coefficient of the HS currents.We insist in directly computing the free correlators from bulk graphs with theunconventional branch. The three-point function of the scalar bilinear turnsout to be an "extremal" one at d=3. The four-leg bulk exchange graph can beprecisely related to the CPWs of the boundary dual scalar and its shadow. Theflow in the IR by Legendre transforming at leading 1/N, following the patternof double-trace deformations, and the assumption of degeneracy of the hologramlead to the CPWE of the scalar four-point function at IR. Here we confirm someprevious results, obtained from more involved computations of skeleton graphs,as well as extend some of them from d=3 to generic dimension 2

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