3-D Interacting CFTs and Generalized Higgs Phenomenon in Higher Spin Theories on AdS

TL;DR

The paper investigates how the proposed AdS4/Higher-Spin duality explains the IR non-conservation of higher-spin currents in the 3-d $O(N)$ vector model. It identifies a bulk one-loop generalized Higgs mechanism where a Goldstone bound state involving the bulk scalar $\\Sigma$ (with IR dimension $\\Delta_\Sigma=2$) induces masses for all spin-$s>2$ fields, while the graviton remains massless, consistent with a double-trace RG flow $(\phi^a \phi^a)^2$. The mechanism yields masses of order $1/N$ and preserves the UV massless spectrum, tying boundary RG flow to bulk dynamics via boundary-condition changes. This work strengthens the HS/AdS correspondence and points to explicit loop calculations and possible extensions to broader RG flows.

Abstract

We study a duality, recently conjectured by Klebanov and Polyakov, between higher-spin theories on AdS_4 and O(N) vector models in 3-d. These theories are free in the UV and interacting in the IR. At the UV fixed point, the O(N) model has an infinite number of higher-spin conserved currents. In the IR, these currents are no longer conserved for spin s>2. In this paper, we show that the dual interpretation of this fact is that all fields of spin s>2 in AdS_4 become massive by a Higgs mechanism, that leaves the spin-2 field massless. We identify the Higgs field and show how it relates to the RG flow connecting the two CFTs, which is induced by a double trace deformation.