- Title Pages
- Dedication
- Prologue
- 1 Introduction
- 2 Relativistic Invariance
- 3 The Electromagnetic Field
- 4 General Relativity: A Field Theory of Gravitation
- 5 The Physical States
- 6 Relativistic Wave Equations
- 7 Towards a Relativistic Quantum Mechanics
- 8 Functional Integrals and Probabilistic Amplitudes
- 9 Functional Integrals and Quantum Mechanics: Formal Developments
- 10 The Euclidean Functional Integrals
- 11 Fermions and Functional Formalism
- 12 Relativistic Quantum Fields
- 13 Applications
- 14 Geometry and Quantum Dynamics
- 15 Broken Symmetries
- 16 Quantum Field Theory at Higher Orders
- 17 A First Glance at Renormalisation and Symmetry
- 18 Renormalisation of Yang–Mills Theory and BRST Symmetry
- 19 Some Consequences of the Renormalisation Group
- 20 Analyticity Properties of Feynman Diagrams
- 21 Infrared Singularities
- 22 Coherent States and Classical Limit of Quantum Electrodynamics
- 23 Quantum Field Theories with a Large Number of Fields
- 24 The Existence of Field Theories beyond the Perturbation Expansion
- 25 Fundamental Interactions
- 26 Beyond the Standard Model
- 27 Supersymmetry, or the Defence of Scalars
- Appendix A Tensor Calculus
- Appendix B Differential Calculus
- Appendix C Groups and Lie Algebras
- Appendix D A Collection of Useful Formulae
- Appendix E Extract from Maxwell’s <i>A Treatise on Electricity and Magnetism</i>
- Index

# Supersymmetry, or the Defence of Scalars

# Supersymmetry, or the Defence of Scalars

- Chapter:
- (p.784) 27 Supersymmetry, or the Defence of Scalars
- Source:
- From Classical to Quantum Fields
- Author(s):
### Laurent Baulieu

### John Iliopoulos

### Roland Sénéor

- Publisher:
- Oxford University Press

The only fields of the Standard Model whose masses are not protected by a symmetry are the scalar fields. Supersymmetry is a symmetry between fermions and bosons which provides precisely such a protection mechanism. This chapter presents a comprehensive study of supersymmetric field theories. In particular, it is shown that they do not suffer from the phenomenon of gauge hierarchy. They have remarkable renormalisation properties and offer the most attractive framework to build a unified theory. The breaking of supersymmetry, both explicit and spontaneous, is studied in detail. The generalisation of electric-magnetic duality in supersymmetric theories yields non-perturbative results and the concept of twist makes possible the study of topological field theories. The supersymmetric extension of the Standard Model is shown to predict the existence of new elementary particles, whose phenomenological properties are analysed.

*Keywords:*
standard model, supersymmetry, gauge hierarchy, renormalisation, fermion, boson, spontaneous breaking, duality, twist, topological theory

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- Title Pages
- Dedication
- Prologue
- 1 Introduction
- 2 Relativistic Invariance
- 3 The Electromagnetic Field
- 4 General Relativity: A Field Theory of Gravitation
- 5 The Physical States
- 6 Relativistic Wave Equations
- 7 Towards a Relativistic Quantum Mechanics
- 8 Functional Integrals and Probabilistic Amplitudes
- 9 Functional Integrals and Quantum Mechanics: Formal Developments
- 10 The Euclidean Functional Integrals
- 11 Fermions and Functional Formalism
- 12 Relativistic Quantum Fields
- 13 Applications
- 14 Geometry and Quantum Dynamics
- 15 Broken Symmetries
- 16 Quantum Field Theory at Higher Orders
- 17 A First Glance at Renormalisation and Symmetry
- 18 Renormalisation of Yang–Mills Theory and BRST Symmetry
- 19 Some Consequences of the Renormalisation Group
- 20 Analyticity Properties of Feynman Diagrams
- 21 Infrared Singularities
- 22 Coherent States and Classical Limit of Quantum Electrodynamics
- 23 Quantum Field Theories with a Large Number of Fields
- 24 The Existence of Field Theories beyond the Perturbation Expansion
- 25 Fundamental Interactions
- 26 Beyond the Standard Model
- 27 Supersymmetry, or the Defence of Scalars
- Appendix A Tensor Calculus
- Appendix B Differential Calculus
- Appendix C Groups and Lie Algebras
- Appendix D A Collection of Useful Formulae
- Appendix E Extract from Maxwell’s <i>A Treatise on Electricity and Magnetism</i>
- Index