TASI lectures on AdS/CFT

Abstract

We introduce the AdS/CFT correspondence as a natural extension of QFT in a fixed AdS background. We start by reviewing some general concepts of CFT, including the embedding space formalism. We then consider QFT in a fixed AdS background and show that one can define boundary operators that enjoy very similar properties as in a CFT, except for the lack of a stress tensor. Including a dynamical metric in AdS generates a boundary stress tensor and completes the CFT axioms. We also discuss some applications of the bulk geometric intuition to strongly coupled QFT. Finally, we end with a review of the main properties of Mellin amplitudes for CFT correlation functions and their uses in the context of AdS/CFT.

63 pages, 7 figures

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• The Large N Limit of Superconformal Field Theories and Supergravity
• Large N Field Theories, String Theory and Gravity
• Holographic Derivation of Entanglement Entropy from AdS/CFT
• M Theory As A Matrix Model: A Conjecture
• A Stress Tensor for Anti-de Sitter Gravity
• Wilson loops in large N field theories
• Lectures on holographic methods for condensed matter physics
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• Black Holes: Complementarity or Firewalls?
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• Implications of Conformal Invariance in Field Theories for General Dimensions
• Holography from Conformal Field Theory
• Conformal collider physics: Energy and charge correlations
• Conformal Four Point Functions and the Operator Product Expansion
• Scattering of Massless Particles in Arbitrary Dimension
• Holographic c-theorems in arbitrary dimensions
• Wilson Loops in N=4 Supersymmetric Yang--Mills Theory
• Holographic duality with a view toward many-body physics
• Writing CFT correlation functions as AdS scattering amplitudes
• Causality Constraints on Corrections to the Graviton Three-Point Coupling
• What is the Simplest Quantum Field Theory?
• The Analytic Bootstrap and AdS Superhorizon Locality
• Spinning Conformal Correlators
• On the RG running of the entanglement entropy of a circle
• Conformal Regge theory
• Graviton exchange and complete 4-point functions in the AdS/CFT correspondence
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• Minimal Model Holography
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• Emergent Spacetime and Holographic CFTs
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• Correlation Functions of Large N Chern-Simons-Matter Theories and Bosonization in Three Dimensions
• Monte Carlo studies of supersymmetric matrix quantum mechanics with sixteen supercharges at finite temperature
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• Towards Feynman rules for Mellin amplitudes in AdS/CFT
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• Structure Constants and Integrable Bootstrap in Planar N=4 SYM Theory
• Holographic description of quantum black hole on a computer
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• Analytic bootstrap at large spin
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Cited by in corpus (48)

• 4D Scattering Amplitudes and Asymptotic Symmetries from 2D CFT
• A Mellin space approach to the conformal bootstrap
• Universality at large transverse spin in defect CFT
• Gravitational Thermodynamics of Causal Diamonds in (A)dS
• Nonperturbative Mellin Amplitudes: Existence, Properties, Applications
• Momentum space approach to crossing symmetric CFT correlators
• Carving Out the End of the World or (Superconformal Bootstrap in Six Dimensions)
• Precision test of AdS${}_6$/CFT${}_5$ in Type IIB
• Momentum space conformal three-point functions of conserved currents and a general spinning operator
• Witten Diagrams for Torus Conformal Blocks
• Exploring The Holographic Swampland
• Gravitational Production of a Conformal Dark Sector
• Towards the higher point holographic momentum space amplitudes II: Gravitons
• Scalar quasinormal modes of Kerr-AdS${}_5$
• Thermal Conformal Blocks
• Looking for (and not finding) a bulk brane
• Quantum Information Scrambling: From Holography to Quantum Simulators
• Putting the Boot into the Swampland
• General null asymptotics and superrotation-compatible configuration spaces in $d\ge 4$
• Tensors and Spinors in de Sitter Space
• Mellin Amplitudes for Fermionic Conformal Correlators
• Moduli Stabilisation and the Holographic Swampland
• Celestial Leaf Amplitudes
• Hamiltonian truncation in Anti-de Sitter spacetime
• On the Exchange Interactions in Holographic p-adic CFT
• Holographic solar systems and hydrogen atoms: non-relativistic physics in AdS and its CFT dual
• Towards the higher point holographic momentum space amplitudes
• All the entropies on the light-cone
• Asymptotic Symmetries, Holography and Topological Hair
• Revisiting Extremal Couplings in AdS/CFT
• Mixed Correlator Dispersive CFT Sum Rules
• Higher-spin gauge theories in three spacetime dimensions
• Bootstrapping Witten diagrams via differential representation in Mellin space
• The High Energy Behavior of Mellin Amplitudes
• Comments on spinning OPE blocks in AdS${}_3$/CFT${}_2$
• Wilson Action for the $O(N)$ Model
• Effective Thermal Physics in Holography: A Brief Review
• Endpoint contributions to excited-state modular Hamiltonians
• Bulk Gauge Fields and Holographic RG from Exact RG
• BCJ Amplitude Relations for Anti-de Sitter Boundary Correlators in Embedding Space
• Comparing top-down and bottom-up holographic defects and boundaries
• Higher spin swampland conjecture for massive AdS${}_3$ gravity
• QCD, with Strings Attached
• Finite Cutoff CFT's and Composite Operators
• QFT on Fuzzy AdS Spaces: Classical Limit and Boundary Correlation Functions
• Holographic RG and Exact RG in O(N) Model
• Holographic metals at finite doping
• On-shell Correlators and Color-Kinematics Duality in Curved Symmetric Spacetimes