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.

arXiv commentv2: 79 pages, 8 figures. Minor changes, references added

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• A universal result on central charges in the presence of double-trace deformations
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• Baryons, monopoles and dualities in Chern-Simons-matter theories
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• One Loop Tests of Higher Spin AdS/CFT
• Quartic AdS Interactions in Higher-Spin Gravity from Conformal Field Theory
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• Character Formulae and Partition Functions in Higher Dimensional Conformal Field Theory
• Higher Spin Interactions in Four Dimensions: Vasiliev vs. Fronsdal
• Elements of Vasiliev theory
• On Higher Spin Gauge Theory and the Critical O(N) Model
• Higher Spin AdS${}_{d+1}$/CFT${}_d$ at One Loop
• Partition Functions and Casimir Energies in Higher Spin AdS_{d+1}/CFT_d
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• The N=4 Quantum Conformal Algebra
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• Supersymmetric Chern-Simons Theories with Vector Matter
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• Supergravity one-loop corrections on AdS_7 and AdS_3, higher spins and AdS/CFT
• Vector Models in the Singlet Sector at Finite Temperature
• Exceptional F(4) Higher-Spin Theory in AdS(6) at One-Loop and other Tests of Duality
• Theory of higher spin tensor currents and central charges
• Geometry and Observables in Vasiliev's Higher Spin Gravity
• Exact higher-spin symmetry in CFT: free fermion correlators from Vasiliev Theory
• A minimal BV action for Vasiliev's four-dimensional higher spin gravity
• Partition Functions for Higher-Spin theories in AdS
• Comments on higher-spin holography
• Constraining conformal field theories with a higher spin symmetry in d=4
• The Holographic Geometry of the Renormalization Group and Higher Spin Symmetries
• A test of bosonization at the level of four-point functions in Chern-Simons vector models
• The Exact Renormalization Group and Higher-spin Holography
• On the Algebraic Structure of Higher-Spin Field Equations and New Exact Solutions
• Mixed-symmetry tensor conserved currents and AdS/CFT correspondence
• One-loop Test of Free SU(N) Adjoint Model Holography
• 1/N and Loop Corrections in Higher Spin AdS_4/CFT_3 Duality
• Towards a gravity dual of the unitary Fermi gas
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• Bi-local Model of AdS/CFT and Higher Spin Gravity
• An action for higher spin gauge theory in four dimensions
• Higher Spin Holography, RG, and the Light Cone
• Invariant Functionals in Higher-Spin Theory

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• Partially Massless Fields During Inflation
• A Holographic Derivation of the Weak Gravity Conjecture
• On the Higher-Spin Spectrum in Large N Chern-Simons Vector Models
• Four loop renormalization of the Gross-Neveu model
• Notes on Spinning Operators in Fermionic CFT
• Tackling the SDC in AdS with CFTs
• Flows, Fixed Points and Duality in Chern-Simons-matter theories
• Generalized Chern-Simons higher-spin gravity theories in three dimensions
• Chern-Simons Matter Theories and Higher Spin Gravity
• Phase diagram and fixed points of tensorial Gross-Neveu models in three dimensions
• Four-point functions in large $N$ Chern-Simons fermionic theories
• AdS one-loop partition functions from bulk and edge characters
• Non-supersymmetric AdS and the Swampland
• On the Higher Spin Spectrum of Chern-Simons Theory coupled to Fermions in the Large Flavour Limit
• Duality and an exact Landau-Ginzburg potential for quasi-bosonic Chern-Simons-Matter theories
• Galilean contractions of $W$-algebras
• ABJ Quadrality
• On special quartic interaction of higher spin gauge fields with scalars and gauge symmetry commutator in the linear approximation
• Equation of motion of canonical tensor model and Hamilton-Jacobi equation of general relativity
• Constraints for Three-Dimensional Higher-Spin Interactions and Conformal Correlators
• Cubic Interaction for Higher Spins in $Ad{S}_{d+1}$ space in the explicit covariant form
• One Loop Tests of Supersymmetric Higher Spin $Ad{S}_4/CF{T}_3$
• The Analytic Bootstrap in Fermionic CFTs
• Comments on spinning OPE blocks in AdS${}_3$/CFT${}_2$
• Tidal excitation as mixing in thermal CFT
• Non-analyticity of holographic Rényi entropy in Lovelock gravity
• Demystifying integrable QFTs in AdS: No-go theorems for higher-spin charges
• A String Dual for Partially Topological Chern-Simons-Matter Theories
• QCD, with Strings Attached
• 3d Large $N$ Vector Models at the Boundary
• Critical structure and emergent symmetry of Dirac fermion systems
• Induced Action for Conformal Higher Spins from Worldline Path Integrals
• Analytic Studies of Fermions in the Conformal Bootstrap
• Quench Disorder and Scalar Field Theory in the Presence of Boundary