Conformal Field Theory for Particle Physicists: From QFT Axioms to the Modern Conformal Bootstrap

Preface
Contents
Acronyms
1 Introduction
References
2 Classical Conformal Transformations
2.1 Infinitesimal Transformations
2.2 The Conformal Algebra
2.3 Finite Transformations
2.4 Compactifications
2.5 Minkowski Space-Time
2.6 Conformal Symmetry in Classical Field Theory
Reference
3 Conformal Quantum Field Theory
3.1 Non-Perturbative Quantum Field Theory
3.2 Wightman Functions
3.3 Spectral Representation
3.4 Scale Symmetry
3.5 Special Conformal Symmetry
3.6 UV/IR Divergences and Anomalies
Reference
4 Conformal Correlation Functions
4.1 From Minkowksi Space-Time to Euclidean Space
4.2 From Euclidean Space to Embedding Space
4.3 3-Point Functions
4.4 4-Point Functions
References
5 State-Operator Correspondence and OPE
5.1 The OPE in Quantum Field Theory
5.2 The State/Operator Correspondence
5.3 The Conformal OPE
6 The Conformal Bootstrap
6.1 Conformal Blocks
6.2 OPE Convergence
6.3 The Crossing Equation and Simple Solutions
6.4 The Numerical Bootstrap
6.5 Example: The Ising Model in 3 Dimensions
6.6 Other Conformal Bootstrap Results
References
7 Outlook
References