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Advanced Topics in Quantum Field Theory

Book Description

Since the advent of Yang-Mills theories and supersymmetry in the 1970s, quantum field theory - the basis of the modern description of physical phenomena at the fundamental level - has undergone revolutionary developments. This is the first systematic and comprehensive text devoted specifically to modern field theory, bringing readers to the cutting edge of current research. The book 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. Featuring extensive cross-referencing from traditional topics to recent breakthroughs in the field, it prepares students for independent research. The side boxes summarizing the main results and over 70 exercises make this an indispensable book for graduate students and researchers in theoretical physics.

Table of Contents

  1. Cover
  2. Half Title
  3. Title Page
  4. Copyright
  5. Dedication
  6. Contents
  7. Preface
    1. References for the Preface
  8. Acknowledgments
  9. Conventions, notation, useful general formulas, abbreviations
  10. Introduction
    1. References for the Introduction
  11. Part I: Before supersymmetry
    1. 1. Phases of gauge theories
      1. 1 Spontaneous symmetry breaking
      2. 2 Spontaneous breaking of gauge symmetries
      3. 3 Phases of Yang–Mills theories
      4. 4 Appendix: Basics of conformal invariance
      5. References for Chapter 1
    2. 2. Kinks and domain walls
      1. 5 Kinks and domain walls (at the classical level)
      2. 6 Higher discrete symmetries and wall junctions
      3. 7 Domain walls antigravitate
      4. 8 Quantization of solitons (kink mass at one loop)
      5. 9 Charge fractionalization
      6. References for Chapter 2
    3. 3. Vortices and flux tubes (strings)
      1. 10 Vortices and strings
      2. 11 Non-Abelian vortices or strings
      3. 12 Fermion zero modes
      4. 13 String-induced gravity
      5. 14 Appendix: Calculation of the orientational part of the world-sheet action for non-Abelian strings
      6. References for Chapter 3
    4. 4. Monopoles and Skyrmions
      1. 15 Magnetic monopoles
      2. 16 Skyrmions
      3. 17 Appendix: Elements of group theory for SU(N)
      4. References for Chapter 4
    5. 5. Instantons
      1. 18 Tunneling in non-Abelian Yang–Mills theory
      2. 19 Euclidean formulation of QCD
      3. 20 BPST instantons: general properties
      4. 21 Explicit form of the BPST instanton
      5. 22 Applications: Baryon number nonconservation at high energy
      6. 23 Instantons at high energies
      7. 24 Other ideas concerning baryon number violation
      8. 25 Appendices
      9. References for Chapter 5
    6. 6. Isotropic (anti)ferromagnet: O(3) sigma model and extensions, including CP(N - 1)
      1. 26 O(3) sigma model
      2. 27 Extensions: CP(N – 1) models
      3. 28 Asymptotic freedom in the O(3) sigma model
      4. 29 Instantons in CP(1)
      5. 30 The Goldstone theorem in two dimensions
      6. References for Chapter 6
    7. 7. False-vacuum decay and related topics
      1. 31 False-vacuum decay
      2. 32 False-vacuum decay: applications
      3. References for Chapter 7
    8. 8. Chiral anomaly
      1. 33 Chiral anomaly in the Schwinger model
      2. 34 Anomalies in QCD and similar non-Abelian gauge theories
      3. 35 ’t Hooft matching and its physical implications
      4. 36 Scale anomaly
      5. References for Chapter 8
    9. 9. Confinement in 4D gauge theories and models in lower dimensions
      1. 37 Confinement in non-Abelian gauge theories: dual Meissner effect
      2. 38 The ’t Hooft limit and 1/N expansion
      3. 39 Abelian Higgs model in 1 + 1 dimensions
      4. 40 CP(N – 1) at large N
      5. 41 The ’t Hooft model
      6. 42 Polyakov’s confinement in 2 + 1 dimensions
      7. 43 Appendix: Solving the O(N) model at large N
      8. References for Chapter 9
  12. Part II: Introduction to supersymmetry
    1. 10. Basics of supersymmetry with emphasis on gauge theories
      1. 44 Introduction
      2. 45 Spinors and spinorial notation
      3. 46 The Coleman–Mandula theorem
      4. 47 Superextension of the Poincaré algebra
      5. 48 Superspace and superfields
      6. 49 Superinvariant actions
      7. 50 R symmetries
      8. 51 Nonrenormalization theorem for F terms
      9. 52 Super-Higgs mechanism
      10. 53 Spontaneous breaking of supersymmetry
      11. 54 Goldstinos
      12. 55 Digression: Two-dimensional supersymmetry
      13. 56 Supersymmetric Yang–Mills theories
      14. 57 Supersymmetric gluodynamics
      15. 58 One-flavor supersymmetric QCD
      16. 59 Hypercurrent and anomalies
      17. 60 R parity
      18. 61 Extended supersymmetries in four dimensions
      19. 62 Instantons in supersymmetric Yang–Mills theories
      20. 63 Affleck–Dine–Seiberg superpotential
      21. 64 Novikov–Shifman–Vainshtein–Zakharov β function
      22. 65 The Witten index
      23. 66 Soft versus hard explicit violations of supersymmetry
      24. 67 Central charges
      25. 68 Long versus short supermultiplets
      26. 69 Appendices
      27. References for Chapter 10
    2. 11. Supersymmetric solitons
      1. 70 Central charges in superalgebras
      2. 71 N = 1: supersymmetric kinks
      3. 72 N = 2: kinks in two-dimensional supersymmetric CP(1) model
      4. 73 Domain walls
      5. 74 Vortices in D = 3 and flux tubes in D = 4
      6. 75 Critical monopoles
      7. References for Chapter 11
  13. Index