The Higher Spin/Vector Model Duality

TL;DR

The article surveys the holographic duality between Vasiliev's AdS4 higher spin theory and large-N vector models, focusing on the computation of boundary correlators and their matching to free/critical vector theories and Chern-Simons vector models. It outlines the frame-like Vasiliev formulation, master fields, and perturbation theory necessary to extract three-point functions, detailing both physical-space and gauge-function approaches and highlighting parity-invariant and parity-violating cases. The work reports new results on parity-odd contributions to three-point functions and discusses ambiguities in gauge choices and contour regularization, emphasizing how θ0 governs bulk couplings and boundary structures. It also sketches extensions to non-Abelian Chan-Paton factors and supersymmetric versions, and discusses open issues in quantization, boundary conditions, and potential 3d bosonization, situating the duality within a broader landscape including AdS3/CFT2 and string-theoretic connections.

Abstract

This paper is mainly a review of the dualities between Vasiliev's higher spin gauge theories in AdS4 and three dimensional large N vector models, with focus on the holographic calculation of correlation functions of higher spin currents. We also present some new results in the computation of parity odd structures in the three point functions in parity violating Vasiliev theories.

Figures (1)

• Figure 1: Extracting the three-point function from the boundary behavior of the second order field sourced by $J_{s_1}$, $J_{s_2}$.