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

We determine the scaling dimensions in the boundary ${\mathsf{C}\mathsf{F}\mathsf{T}}_d$ corresponding to the $\mathsf{O}(N)$ model in ${\mathsf{E}\mathsf{A}\mathsf{d}\mathsf{S}}_{d+1}$. The $\mathsf{C}\mathsf{F}\mathsf{T}$ 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 $1\mathrm{/}N$ expansion. We focus on the non-singlet sectors, namely the anti-symmetric and symmetric traceless irreducible representations of the $\mathsf{O}(N)$ 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 $1\mathrm{/}N$ corrections to the $\mathsf{C}\mathsf{F}\mathsf{T}$ data in the interacting theory.