On (Un)Broken Higher-Spin Symmetry in Vector Models

TL;DR

<p>We analyze how higher-spin (HS) symmetry constrains vector-model CFTs and how its breaking modifies the HS current spectrum. Using multiplet recombination in the Wilson-Fisher CFT, we extract one-loop anomalous dimensions of HS currents in both the $4-\epsilon$ and large-$N$ regimes, tying the results to non-conservation operators $K$ and the associated double/triple-trace structures. The work then connects these CFT results to holographic AdS duals, reconstructing parts of the HS cubic action and predicting one-loop bulk mass shifts for HS fields, with a unified HS-algebra interpretation via $hs(\lambda)$ and generalized free-field structures. The findings support a deep link between HS symmetry breaking in the boundary CFT and mass deformations in the bulk HS theory, and they offer concrete data to test HS-AdS/CFT proposals across dimensions. </p>

Abstract

The simplest consequences of exact and broken higher-spin symmetry are studied. The one-loop anomalous dimensions of higher-spin currents are determined from the multiplet recombination in the spirit of the modern bootstrap programme: the Wilson-Fisher CFT is studied both in the epsilon-expansion and in the large-N. The bulk implications are briefly addressed: part of the higher-spin theory cubic action is reconstructed; one-loop corrections to the AdS masses of higher-spin fields are discussed.