TASI Lectures on AdS/CFT

2016/08/17 by Joao Penedones, João Penedones · 1 voice · 3 citations
Physics and Astronomy · #Anti-de Sitter space #Black Holes and Theoretical Physics #Computer science #Cosmology and Gravitation Theories #Embedding #Mathematical physics #Noncommutative and Quantum Gravity Theories #Physics #Spinor #Theoretical physics #hep-th

paper · pdf · doi:10.1142/9789813149441_0002

63 pages, 7 figures

arxiv created 2016/08/17 · openalex publication_date 2016/11/21 · arxiv updated 2016/12/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

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.

Citations

• Structure Constants and Integrable Bootstrap in Planar N=4 SYM Theory
• Conformal collider physics: Energy and charge correlations
• Correlation functions of large N Chern-Simons-Matter theories and bosonization in three dimensions
• Viscosity Information from Relativistic Nuclear Collisions: How Perfect is the Fluid Observed at RHIC?
• Implications of Conformal Invariance in Field Theories for General Dimensions
• Thermodynamics of black holes in anti-de Sitter space
• Holographic Derivation of Entanglement Entropy from the anti–de Sitter Space/Conformal Field Theory Correspondence
• Holographic Duality with a View Toward Many‐Body Physics
• Mtheory as a matrix model: A conjecture
• A planar diagram theory for strong interactions
• Lecture Notes on Holographic Renormalization
• The Large-N Limit of Superconformal Field Theories and Supergravity
• TASI Lectures on the Conformal Bootstrap

Cited by

• Scalar quasinormal modes of Kerr−AdS5
• Carving out the end of the world or (superconformal bootstrap in six dimensions)
• Comparing top-down and bottom-up holographic defects and boundaries
• Charged Penrose Extraction in RN--AdS Black Holes with Dark Energy: Ergosphere Geometry and Rigorous Efficiency Bounds

Discussions

• Hints to prove $^1$ eq. (6) in Ref. 1: Hilbert/metric SEM tensor in Euclidean signature : $$T^{\mu\nu}(x)~:=~ -\frac{2}{\sqrt{g(x)}}\frac{\delta S[\phi;g]}{\delta g_{\mu\nu}(x)}.\tag{A}$$ Lie derivati [stackexchange, 1 points]

Related

• QFT in AdS instead of LSZ
• AdS/CFT correspondence for n-point functions
• Operator Dictionaries and Wave Functions in AdS/CFT and dS/CFT
• AdS/CFT Correspondence Beyond its Supergravity Approximation
• Some Aspects of the AdS/CFT Correspondence