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

TL;DR

This paper explores a duality between higher-spin theories in AdS_4 and 3D O(N) vector models, showing how a Higgs mechanism explains the mass acquisition of higher-spin fields during the RG flow from UV to IR.

Contribution

It provides a detailed holographic interpretation of the Higgs phenomenon for higher-spin fields in AdS_4, linked to the RG flow in the dual CFTs induced by a double trace deformation.

Findings

Higher-spin fields s>2 become massive in the IR

The Higgs mechanism explains the breaking of higher-spin symmetries

RG flow connects UV free and IR interacting fixed points

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.