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

TL;DR

This work computes boundary CFT data for the O(N) model in AdS with unbroken symmetry at finite bulk coupling, extracting leading 1/N corrections in d=2 and d=4. It develops a framework that combines the spectral representation of the sigma propagator, conformal partial waves, and 6j-symbol crossing kernels to relate crossed-channel t-channel data to the s-channel double-twist spectrum, focusing on non-singlet (ST and AS) representations. The authors derive general formulas for the t-channel contributions to anomalous dimensions in 2d and 4d, and they perform numerical analysis to map the non-singlet twist–spin trajectories, examining large-n and large-J behavior and identifying coupling-dependent shifts. They also discuss renormalization subtleties, potential bulk criticality, and extensions to BCFT/DCFT contexts, underscoring the role of finite-coupling AdS/CFT as a rich setting for cross-channel consistency checks and spectrum generation.

Abstract

We determine the scaling dimensions in the boundary $\mathsf{CFT}_{d}$ corresponding to the $\mathsf{O}(N)$ model in $\mathsf{EAdS}_{d+1}$. The $\mathsf{CFT}$ 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 $\mathsf{O}(N)$ 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 $1/N$ corrections to the $\mathsf{CFT}$ data in the interacting theory.