Table of Contents
Contents
Acknowledgments
Chapter 1 Introduction
1.1 What is Supersymmetry, and Why is it Exciting (the Short Version)?
1.2 What This Book is and What it is Not
1.3 Effective Field Theories, Naturalness, and the Higgs Mass
1.4 Further Reading
Chapter 2 A Crash Course on Weyl Spinors
2.1 Brief Review of the Dirac Equation and of Some Matrix Properties
2.2 Weyl versus Dirac Spinors
2.3 Helicity
2.4 Lorentz Transformations and Invariants
2.5 A First Notational Hurdle
2.6 Building More Lorentz Invariants Out of Weyl Spinors
2.7 Invariants Containing Lorentz Indices
2.8 A Useful Identity
2.9 Introducing a New Notation
2.10 Quiz
Chapter 3 New Notation for the Components of Weyl Spinors
3.1 Building Lorentz Invariants
3.2 Index-Free Notation
3.3 Invariants Built Out of Two Left-Chiral Spinors
3.4 The ∈ Notation for ±iσ[sup(2)]
3.5 Notation for the Indices of σ[sup(μ)] and σ[sup(μ)]
3.6 Quiz
Chapter 4 The Physics of Weyl, Majorana, and Dirac Spinors
4.1 Charge Conjugation and Antiparticles for Dirac Spinors
4.2 CPT Invariance
4.3 A Massless Weyl Spinor
4.4 Adding a Mass: General Considerations
4.5 Adding a Mass: Dirac Spinors
4.6 The QED Lagrangian in Terms of Weyl Spinors
4.7 Adding a Mass: Majorana Spinors
4.8 Dirac Spinors and Parity
4.9 Definition of the Masses of Scalars and Spinor Fields
4.10 Adding a Mass: Weyl Spinor
4.11 Relation Between Weyl Spinors and Majorana Spinors
4.12 Quiz
Chapter 5 Building the Simplest Supersymmetric Lagrangian
5.1 Dimensional Analysis
5.2 The Transformation of the Fields
5.3 Transformation of the Lagrangian
5.4 Quiz
Chapter 6 The Supersymmetric Charges and Their Algebra
6.1 Charges: General Discussion
6.2 Explicit Representations of the Charges and the Charge Algebra
6.3 Finding the Algebra Without the Explicit Charges
6.4 Example
6.5 The SUSY Algebra
6.6 Nonclosure of the Algebra for the Spinor Field
6.7 Introduction of an Auxiliary Field
6.8 Closure of the Algebra
6.9 Quiz
Chapter 7 Applications of the SUSY Algebra
7.1 Classification of States Using the Algebra: Review of the Poincaé Group
7.2 Effects of the Supercharges on States
7.3 The Massless SUSY Multiplets
7.4 Massless SUSY Multiplets and the MSSM
7.5 Two More Important Results
7.6 The Algebra in Majorana Form
7.7 Obtaining the Charges from Symmetry Currents
7.8 Explicit Supercharges as Quantum Field Operators
7.9 The Coleman-Mandula No-Go Theorem
7.10 The Haag-Lopuszanski-Sohnius Theorem and Extended SUSY
7.11 Quiz
Chapter 8 Adding Interactions: The Wess-Zumino Model
8.1 A Supersymmetric Lagrangian With Masses and Interactions
8.2 A More General Lagrangian
8.3 The Full Wess-Zumino Lagrangian
8.4 The Wess-Zumino Lagrangian in Majorana Form
8.5 Quiz
Chapter 9 Some Explicit Calculations
9.1 Refresher About Calculations of Processes in Quantum Field Theory
9.2 Propagators
9.3 One Point Function
9.4 Propagator of the B Field to One Loop
9.5 Putting It All Together
9.6 A Note on Nonrenormalization Theorems
9.7 Quiz
Chapter 10 Supersymmetric Gauge Theories
10.1 Free Supersymmetric Abelian Gauge Theory
10.2 Introduction of the Auxiliary Field
10.3 Review of Nonabelian Gauge Theories
10.4 The QCD Lagrangian in Terms of Weyl Spinors
10.5 Free Supersymmetric Nonabelian Gauge Theories
10.6 Combining an Abelian Vector Multiplet With a Chiral Multiplet
10.7 Eliminating the Auxiliary Fields
10.8 Combining a Nonabelian Gauge Multiplet With a Chiral Multiplet
10.9 Quiz
Chapter 11 Superspace Formalism
11.1 The Superspace Coordinates
11.2 Example of Spacetime Translations
11.3 Supersymmetric Transformations of the Superspace Coordinates
11.4 Introduction to Superfields
11.5 Aside on Grassmann Calculus
11.6 The SUSY Charges as Differential Operators
11.7 Constraints and Superfields
11.8 Quiz
Chapter 12 Left-Chiral Superfields
12.1 General Expansion of Left-Chiral Superfields
12.2 SUSY Transformations of the Component Fields
12.3 Constructing SUSY Invariants Out of Left-Chiral Superfields
12.4 Relation Between the Superpotential in Terms of Super.elds and the Superpotential of Chapter 8
12.5 The Free Part of the Wess-Zumino Model
12.6 Why Does It All Work?
12.7 Quiz
Chapter 13 Supersymmetric Gauge Field Theories in the Superfield Approach
13.1 Abelian Gauge Invariance in the Superfield Formalism
13.2 Explicit Interactions Between a Left-Chiral Multiplet and the Abelian Gauge Multiplet
13.3 Lagrangian of a Free Supersymmetric Abelian Gauge Theory in Superfield Notation
13.4 The Abelian Field-Strength Superfield in Terms of Component Fields
13.5 The Free Abelian Supersymmetric Lagrangian from the Superfield Approach
13.6 Supersymmetric QED
13.7 Supersymmetric Nonabelian Gauge Theories
13.8 Quiz
Chapter 14 SUSY Breaking
14.1 Spontaneous Supersymmetry Breaking
14.2 F-Type SUSY Breaking
14.3 The O’Raifeartaigh Model
14.4 Mass Spectrum: General Considerations
14.5 Mass Spectrum of the O’Raifeartaigh Model for Μ[sup(2) ≥ 2g2Μ[sup(2)]
14.6 The Supertrace
14.7 D-Type SUSY Breaking
14.8 Second Example of D-Type SUSY Breaking
14.9 Explicit SUSY Breaking
14.10 Quiz
Chapter 15 Introduction to the Minimal Supersymmetric Standard Model
15.1 Lightning Review of the Standard Model
15.2 Spontaneous Symmetry Breaking in the Standard Model
15.3 Aside on Notation
15.4 The Left-Chiral Superfields of the MSSM
15.5 The Gauge Vector Superfields
15.6 The MSSM Lagrangian
15.7 The Superpotential of the MSSM
15.8 The General MSSM Superpotential
15.9 Quiz
Chapter 16 Some Phenomenological Implications of the MSSM
16.1 Supersymmetry Breaking in the MSSM
16.2 The Scalar Potential, Electroweak Symmetry Breaking, and All That
16.3 Finding a Minimum
16.4 The Masses of the Gauge Bosons
16.5 Masses of the Higgs
16.6 Masses of the Leptons, Quarks, and Their Superpartners
16.7 Some Other Consequences of the MSSM
16.8 Coupling Unification in Supersymmetric GUT
16.9 Quiz
Final Exam
References
Appendix A: Useful Identities
Appendix B: Solutions to Exercises
Appendix C: Solutions to Quizzes
Appendix D: Solutions to Final Exam
Index
A
B
C
D
E
F
G
H
I
J
K
L
M
N
O
P
Q
R
S
T
V
W
Y
Z
