TASI Lectures on the Higher Spin - CFT duality

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.

v2: 79 pages, 8 figures. Minor changes, references added

References in corpus (14)

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• Holographic c-theorems in arbitrary dimensions
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• Seiberg Duality in Chern-Simons Theory
• Critical $O(N)$ Models in $6-\epsilon$ Dimensions
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• Three Loop Analysis of the Critical $O(N)$ Models in $6-\epsilon$ Dimensions
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• Supergravity one-loop corrections on AdS_7 and AdS_3, higher spins and AdS/CFT
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Cited by in corpus (9)

• Four loop renormalization of the Gross-Neveu model
• ABJ Quadrality
• Equation of motion of canonical tensor model and Hamilton-Jacobi equation of general relativity
• One Loop Tests of Supersymmetric Higher Spin $Ad{S}_4/CF{T}_3$
• Tidal excitation as mixing in thermal CFT
• QCD, with Strings Attached
• Induced Action for Conformal Higher Spins from Worldline Path Integrals
• Quench Disorder and Scalar Field Theory in the Presence of Boundary
• Analytic Studies of Fermions in the Conformal Bootstrap