Book contents
- Frontmatter
- Dedication
- Contents
- Preface
- Acknowledgments
- Introduction
- Part I Formalism
- 1 Introduction to general relativity 1: Kinematics and Einstein equations
- 2 Introduction to general relativity 2: Vielbein and spin connection, anti-de Sitter space, black holes
- 3 Introduction to supersymmetry 1:Wess–Zumino models, on-shell and off-shell supersymmetry
- 4 Introduction to supersymmetry 2:Multiplets and extended supersymmetry
- 5 Introduction to supersymmetry 3: Superspace formalism in d = 4: Perturbative susy breaking
- 6 Four-dimensional on-shell supergravity and how to count degrees of freedom
- 7 Three-dimensional N = 1 off-shell supergravity
- 8 Coset theory and rigid superspace
- 9 Covariant formulation of YM in rigid superspace and local superspace formalisms
- 10 N = 1 Four-dimensional off-shell supergravity
- 11 N = 1 Four-dimensional supergravity in superspace
- 12 Superspace actions and coupling supergravity with matter
- 13 Kaluza–Klein (KK)-dimensional reduction and examples
- 14 Spherical harmonics and the KK expansion on sphere, coset, and group spaces
- 15 N = 2 sugra in 4 dimensions, general sugra theories, and N = 1 sugra in 11 dimensions
- Part II Applications
- References
- Index
9 - Covariant formulation of YM in rigid superspace and local superspace formalisms
from Part I - Formalism
Published online by Cambridge University Press: 14 November 2024
Book contents
- Frontmatter
- Dedication
- Contents
- Preface
- Acknowledgments
- Introduction
- Part I Formalism
- 1 Introduction to general relativity 1: Kinematics and Einstein equations
- 2 Introduction to general relativity 2: Vielbein and spin connection, anti-de Sitter space, black holes
- 3 Introduction to supersymmetry 1:Wess–Zumino models, on-shell and off-shell supersymmetry
- 4 Introduction to supersymmetry 2:Multiplets and extended supersymmetry
- 5 Introduction to supersymmetry 3: Superspace formalism in d = 4: Perturbative susy breaking
- 6 Four-dimensional on-shell supergravity and how to count degrees of freedom
- 7 Three-dimensional N = 1 off-shell supergravity
- 8 Coset theory and rigid superspace
- 9 Covariant formulation of YM in rigid superspace and local superspace formalisms
- 10 N = 1 Four-dimensional off-shell supergravity
- 11 N = 1 Four-dimensional supergravity in superspace
- 12 Superspace actions and coupling supergravity with matter
- 13 Kaluza–Klein (KK)-dimensional reduction and examples
- 14 Spherical harmonics and the KK expansion on sphere, coset, and group spaces
- 15 N = 2 sugra in 4 dimensions, general sugra theories, and N = 1 sugra in 11 dimensions
- Part II Applications
- References
- Index
Summary
After obtaining the transformation rules and constraints from rigid superspace described as a coset, we define the covariant formulation of four-dimensional YM in rigid superspace and solve the constraints and Bianchi identities, and relate this formulation to the prepotential formalism. Then, we describe the coset approach to three-dimensional supergravity (as a generalization of the covariant YM formalism). Finally, we describe the general super-geometric approach to supergravity.
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- Introduction to Supergravity and its Applications , pp. 100 - 113Publisher: Cambridge University PressPrint publication year: 2024