TASI Lectures on the Higher Spin - CFT duality

TL;DR

This paper reviews the duality between higher spin gravity theories in AdS space and large N vector models, including recent tests and generalizations involving Chern-Simons couplings.

Contribution

It provides a comprehensive overview of the higher spin - CFT duality, including foundational equations, generalizations, and recent computational tests.

Findings

Confirmation of duality through correlation functions

Matching of one-loop partition functions

Extensions to Chern-Simons coupled models

Abstract

In these lectures we give an overview of the duality between gravitational theories of massless higher spin fields in AdS and large N vector models. We first review the original higher spin/vector model duality conjectured by Klebanov and Polyakov, and then discuss its generalizations involving vector models coupled to Chern-Simons gauge fields. We proceed to review some aspects of the theory of massless higher spins, starting with the Fronsdal equations for free fields and moving on to the fully non-linear Vasiliev equations in four dimensions. We end by reviewing some recent tests of the higher spin/vector model duality at the level of correlation functions and one-loop partition functions.