TY - JOUR

T1 - On the AdS higher spin / O(N) vector model correspondence

T2 - Degeneracy of the holographic image

AU - Diaz, Danilo E.

AU - Dorn, Harald

PY - 2006/7/1

Y1 - 2006/7/1

N2 - We explore the conjectured duality between the critical O(N) vector model and minimal bosonic massless higher spin (HS) theory in AdS. In the free boundary 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-point 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.

AB - We explore the conjectured duality between the critical O(N) vector model and minimal bosonic massless higher spin (HS) theory in AdS. In the free boundary 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-point 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.

KW - 1/N Expansion

KW - AdS-CFT Correspondence

KW - Field Theories in Lower Dimensions

UR - http://www.scopus.com/inward/record.url?scp=33748792819&partnerID=8YFLogxK

U2 - 10.1088/1126-6708/2006/07/022

DO - 10.1088/1126-6708/2006/07/022

M3 - Article

AN - SCOPUS:33748792819

SN - 1029-8479

VL - 2006

JO - Journal of High Energy Physics

JF - Journal of High Energy Physics

IS - 7

M1 - 022

ER -