Perturbative and Non-Perturbative Aspects in Vector Model/Higher Spin Duality

TL;DR

This paper reviews recent advances in the AdS/CFT duality involving the 3d O(N) Vector Model and Higher Spin Gravity, focusing on perturbative and non-perturbative aspects using bi-local collective field theory.

Contribution

It introduces a bi-local collective field theory framework that captures both perturbative and non-perturbative features of the higher spin duality, including an exact nonlinear transformation and geometric structure.

Findings

The bulk S-matrix is argued to be trivial (equal to 1).

Nonlinearities in the theory are removable via exact transformations.

A geometric Kahler space framework is developed for the bi-local theory.

Abstract

We review some recent work on AdS/CFT duality involving the 3d O(N) Vector Model and AdS4 Higher Spin Gravity. Our construction is based on bi-local collective field theory which provides an off-shell formulation of Higher Spin Gravity with G = 1/N playing the role of a coupling constant. Consequently perturbative and non-perturbative issues of the theory can be studied. For the correspondence based on free CFT's we discuss the nature of bulk 1/N interactions through an S-matrix which is argued to be equal to 1 (Coleman-Mandula theorem). As a consequence in this class of theories nonlinearities are removable, through a nonlinear field transformation which we show at the exact level. We also describe a geometric (Kahler space) framework for the bi-local theory which applies equally simple to Sp(2N) fermions and the de Sitter correspondence. We discuss in this framework the structure and size of the bi-local Hilbert space and the implementation of (finite N) exclusion principle.