Advanced Topics in Quantum Field Theory: A Lecture Course

Description

Quantum field theory is the basis of our modern description of physical phenomena at the fundamental level. This systematic and comprehensive text emphasizes nonperturbative phenomena and supersymmetry. It includes a thorough discussion of various phases of gauge theories, extended objects and their quantization, and global supersymmetry from a modern perspective. This Second Edition is revised to include topics developed in the last decade, including higher-form global symmetries and their applications, anomalies in supersymmetric theories beyond Ferrara–Zumino, and non-Abelian supersymmetric vortex strings. A new final part is added, presenting more than 90 problems with detailed solutions, allowing students to check their understanding of the acquired knowledge and providing extra details to supplement the main text descriptions. This an indispensable book for graduate students and researchers in theoretical physics. Contents Preface to the Second Edition Preface to the First Edition Acknowledgments Useful General Formulas and Notation, Conventions, Abbreviations Introduction PART I. BEFORE SUPERSYMMETRY 1 Phases of Gauge Theories 1.1 Spontaneous Symmetry Breaking 1.2 Spontaneous Breaking of Gauge Symmetries 1.3 Phases of Yang–Mills Theories 1.4 Appendix: Basics of Conformal Invariance References for Chapter 1 2 Kinks and DomainWalls 2.1 Kinks and DomainWalls (at the Classical Level) 2.2 Higher Discrete Symmetries and Wall Junctions 2.3 Domain Walls Antigravitate 2.4 Quantization of Solitons (Kink Mass at One Loop) 2.5 Charge Fractionalization References for Chapter 2 3 Vortices and Flux Tubes (Strings) 3.1 Vortices and Strings 3.2 Non-Abelian Vortices or Strings 3.3 Fermion Zero Modes 3.4 String-Induced Gravity 3.5 Appendix: Calculation of the Orientational Part of the World-Sheet Action for Non-Abelian Strings 3.6 Appendix: Two-String Junctions and Z Strings in SM References for Chapter 3 4 Monopoles and Skyrmions 4.1 Magnetic Monopoles 4.2 Skyrmions 4.3 Appendix: Elements of Group Theory for SU(N) References for Chapter 4 5 Instantons 5.1 Tunneling in Non-Abelian Yang–Mills Theory 5.2 Euclidean Formulation of QCD 5.3 BPST Instantons: General Properties 5.4 Explicit Form of the BPST Instanton 5.5 Applications: Baryon Number Nonconservation at High Energy 5.6 Instantons at High Energies 5.7 Other Ideas Concerning Baryon Number Violation 5.8 Appendices References for Chapter 5 6 Isotropic (Anti)ferromagnet: O(3) Sigma Model and Extensions, Including CP(N − 1) 6.1 O(3) Sigma Model 6.2 Extensions: CP(N − 1) Models 6.3 Asymptotic Freedom in the O(3) Sigma Model 6.4 Instantons in CP(1) 6.5 The Goldstone Theorem in Two Dimensions References for Chapter 6 7 False-Vacuum Decay and Related Topics 7.1 False-Vacuum Decay 7.2 False-Vacuum Decay: Applications References for Chapter 7 8 Chiral and Other Anomalies 8.1 Chiral Anomaly in the Schwinger Model 8.2 Anomalies in QCD and Similar Non-Abelian Gauge Theories 8.3 ’t Hooft Matching and Its Physical Implications 8.4 Scale Anomaly 8.5 One-Form Anomalies References for Chapter 8 9 Confinement in 4D Gauge Theories and Models in Lower Dimensions 9.1 Confinement in Non-Abelian Gauge Theories: Dual Meissner Effect 9.2 The ’t Hooft Limit and 1/N Expansion 9.3 Abelian Higgs Model in 1 + 1 Dimensions 9.4 CP(N − 1) at Large N 9.5 The ’t Hooft Model 9.6 Schwinger Model 9.7 Polyakov’s Confinement in 2+1 Dimensions 9.8 Appendix: Solving the O(N) Model at Large N References for Chapter 9 PART II. INTRODUCTION TO SUPERSYMMETRY 10. Basics of Supersymmetry with Emphasis on Gauge Theories 10.1 Introduction 10.2 Spinors and Spinorial Notation 10.3 The Coleman–Mandula Theorem 10.4 Superextension of the Poincaré Algebra 10.5 Superspace and Superfields 10.6 Superinvariant Actions 10.7 R Symmetries 10.8 Nonrenormalization Theorem for F Terms 10.9 Super-Higgs Mechanism 10.10 Spontaneous Breaking of Supersymmetry 10.11 Goldstinos 10.12 Digression: Two-Dimensional Supersymmetry 10.13 Supersymmetric Yang–Mills Theories 10.14 Supersymmetric Gluodynamics 10.15 One-Flavor Supersymmetric QCD 10.16 Hypercurrent and Anomalies 10.17 R Parity 10.18 Extended Supersymmetries in Four Dimensions 10.19 Instantons in Supersymmetric Yang–Mills Theories 10.20 Affleck–Dine–Seiberg Superpotential 10.21 Novikov–Shifman–Vainshtein–Zakharov β Function 10.22 The Witten Index 10.23 Q-Closed and Q-Exact Operators 10.24 Soft versus Hard Explicit Violations of Supersymmetry 10.25 Central Charges 10.26 Long versus Short Supermultiplets 10.27 Appendices References for Chapter 10 11 Supersymmetric Solitons 11.1 Central Charges in Superalgebras 11.2 N = 1: Supersymmetric Kinks 11.3 N = 2: Kinks in Two-Dimensional Supersymmetric CP(1) Model 11.4 Domain Walls 11.5 Vortices in D = 3 and Flux Tubes in D = 4 11.6 Critical Monopoles References for Chapter 11 PART III. SOLUTIONS TO EXERCISES Chapter 1 Exercise 1.1.1 , page 19 Exercise 1.3.1, page 34 Chapter 2 Exercise 2.1.1, page 55 Exercise 2.1.2, page 56 Exercise 2.1.3, page 56 Exercise 2.1.4, page 56 Exercise 2.1.5, page 56 Exercise 2.2.1, page 67 Exercise 2.2.2, page 67 Exercise 2.2.3, page 67 Exercise 2.2.4∗, page 67 Exercise 2.3.1, page 72 Exercise 2.3.2∗, page 73 Exercise 2.4.1, page 81 Exercise 2.4.2, page 81 Exercise 2.4.3, page 81 Chapter 3 Exercise 3.1.1, page 99 Exercise 3.2.1, page 109 Exercise 3.2.2, page 109 Exercise 3.4.1, page 118 Chapter 4 Exercise 4.1.1, page 150 Exercise 4.1.2, page 150 Exercise 4.1.3, page 150 Exercise 4.2.1, page 169 Exercise 4.2.2, page 169 Exercise 4.2.3, page 169 Exercise 4.2.4, page 169 Chapter 5 Exercise 5.1.1, page 182 Exercise 5.2.1, page 185 Exercise 5.4.1, page 221 Exercise 5.4.2, page 221 Exercise 5.4.3, page 222 Exercise 5.4.4, page 222 Exercise 5.4.5, page 222 Exercise 5.7.1, page 240 Chapter 6 Exercise 6.2.1, page 256 Exercise 6.2.2, page 257 Exercise 6.2.3, page 257 Exercise 6.3.1, page 266 Exercise 6.3.2, page 266 Exercise 6.3.3, page 266 Exercise 6.4.1, page 269 Exercise 6.5.1, page 273 Chapter 7 Exercise 7.1.1, page 284 Exercise 7.2.1, page 297 Chapter 8 Exercise 8.1.1, page 316 Exercise 8.2.1, page 323 Exercise 8.2.2, page 323 Exercise 8.3.1, page 327 Exercise 8.5.1, page 334 Chapter 9 Exercise 9.4.1, page 374 Exercise 9.4.2, page 374 Exercise 9.5.1, page 387 Exercise 9.5.2, page 387 Exercise 9.6.1, page 392 Chapter 10 Exercise 10.2.1, page 427 Exercise 10.2.2, page 427 Exercise 10.2.3, page 427 Exercise 10.2.4, page 427 Exercise 10.4.1, page 436 Exercise 10.4.2, page 436 Exercise 10.5.1, page 441 Exercise 10.5.2, page 441 Exercise 10.5.3, page 441 Exercise 10.6.1, page 458 Exercise 10.6.2, page 458 Exercise 10.6.3, page 458 Exercise 10.6.4, page 458 Exercise 10.9.1, page 466 Exercise 10.10.1, page 470 Exercise 10.12.1, page 483 Exercise 10.12.2, page 483 Exercises 10.12.3–10.12.6, page 483, 484 Exercises 10.12.7, page 484 Exercise 10.16.1, page 511 Exercise 10.16.2, page 511 Exercise 10.16.3, page 511 Exercise 10.16.4, page 511 Exercise 10.16.5, page 511 Exercise 10.16.6, page 511 Exercise 10.19.1, page 541 Exercise 10.25.1, page 561 Chapter 11 Exercise 11.5.1, page 625 Index abc def ghijk lmnop qrs tuvwyz