Advanced Topics in Quantum Field Theory: A Lecture Course

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
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