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

Description

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