Finite-coupling spectrum of O(N) model in AdS

A bstract We determine the scaling dimensions in the boundary CFT d corresponding to the O( N ) model in EAdS d +1 . The CFT data accessible to the 4-point boundary correlator of fundamental fields are extracted in d = 2 and d = 4, at a finite coupling, and to the leading nontrivial order in the 1 /N expansion. We focus on the non-singlet sectors, namely the anti-symmetric and symmetric traceless irreducible representations of the O( N ) group, extending the previous results that considered only the singlet sector. Studying the non-singlet sector requires an understanding of the crossed-channel diagram contributions to the s -channel conformal block decomposition. Building upon an existing computation, we present general formulas in d = 2 and d = 4 for the contribution of a t -channel conformal block to the anomalous dimensions of s -channel double-twist operators, derived for external scalar operators with equal scaling dimensions. Up to some technical details, this eventually leads to the complete picture of 1 /N corrections to the CFT data in the interacting theory.