Advanced Topics in Quantum Field Theory 2nd Edition by Mikhail Shifman ISBN 9781108840422 1108840426

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 Domain Walls

2.1 Kinks and Domain Walls (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 String

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 mathcal N = 1: Supersymmetric Kinks

11.3 mahtcal 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

Chapter 2

Chapter 3

Chapter 4

Chapter 5

Chapter 6

Chapter 7

Chapter 8

Chapter 9

Chapter 10

Chapter 11

Index