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## Book Description

Supergravity, together with string theory, is one of the most significant developments in theoretical physics. Written by two of the most respected workers in the field, this is the first-ever authoritative and systematic account of supergravity. The book starts by reviewing aspects of relativistic field theory in Minkowski spacetime. After introducing the relevant ingredients of differential geometry and gravity, some basic supergravity theories (D=4 and D=11) and the main gauge theory tools are explained. In the second half of the book, complex geometry and N=1 and N=2 supergravity theories are covered. Classical solutions and a chapter on AdS/CFT complete the book. Numerous exercises and examples make it ideal for Ph.D. students, and with applications to model building, cosmology and solutions of supergravity theories, it is also invaluable to researchers. A website hosted by the authors, featuring solutions to some exercises and additional reading material, can be found at www.cambridge.org/supergravity.

1. Cover
2. Title
4. Contents
5. Preface
6. Acknowledgements
7. Introduction
8. Part I: Relativistic Field Theory in Minkowski Spacetime
1. 1 - Scalar Field Theory and its Symmetries
1. 1.1 The Scalar Field System
2. 1.2 Symmetries of the System
3. 1.3 Noether Currents and Charges
4. 1.4 Symmetries in the Canonical Formalism
5. 1.5 Quantum Operators
6. 1.6 The Lorentz Group for D = 4
2. 2 - The Dirac Field
1. 2.1 The Homomorphism of SL(2, ℂ) → SO(3, 1)
2. 2.2 The Dirac Equation
3. 2.3 Dirac Adjoint and Bilinear Form
4. 2.4 Dirac Action
5. 2.5 The Spinors u(p, s) and υ(p, s) for D = 4
6. 2.6 Weyl Spinor Fields in even Spacetime Dimension
7. 2.7 Conserved Currents
3. 3 - Clifford Algebras and Spinors
1. 3.1 The Clifford Algebra in General Dimension
2. 3.2 Spinors in General Dimensions
3. 3.3 Majorana Spinors
4. 3.4 Majorana Spinors in Physical Theories
5. Appendix 3A Details of the Clifford Algebras for D = 2m
4. 4 - The Maxwell an Yang–Mills gauge fields
1. 4.1 The Abelian Gauge Field Aμ(x)
2. 4.2 Electromagnetic Duality
3. 4.3 Non-Abelian Gauge Symmetry
4. 4.4 Internal Symmetry for Majorana Spinors
5. 5 - The Free Rarita–Schwinger Field
1. 5.1 The Initial Value Problem
2. 5.2 Sources and Green’s Function
3. 5.3 Massive Gravitinos from Dimensional Reduction
6. 6 - N = 1 Global Supersymmetry in D = 4
1. 6.1 Basic SUSY Field Theory
2. 6.2 SUSY Field Theories of the Chiral Multiplet
3. 6.3 SUSY Gauge Theories
4. 6.4 Massless Representations of N-extended Supersymmetry
5. Appendix 6A Extended Supersymmetry and Weyl Spinors
9. Part II: Differential Geometry and Gravity
1. 7 - Differential Geometry
1. 7.1 Manifolds
2. 7.2 Scalars, Vectors, Tensors, etc.
3. 7.3 The Algebra and Calculus of Differential Forms
4. 7.4 The Metric and Frame Field on a Manifold
5. 7.5 Volume Forms and Integration
6. 7.6 Hodge Duality of Forms
7. 7.7 Stokes’ Theorem and Electromagnetic Charges
8. 7.8 p-Form gauge fields
9. 7.9 Connections and Covariant Derivatives
10. 7.10 The Second Structure Equation and the Curvature Tensor
11. 7.11 The Nonlinear σ-model
12. 7.12 Symmetries and Killing Vectors
2. 8 - The First and Second Order Formulations of General Relativity
10. Part III: Basic Supergravity
1. 9 - N = 1 Pure Supergravity in Four Dimensions
2. 10 - D = 11 Supergravity
3. 11 - General Gauge Theory
1. 11.1 Symmetries
2. 11.2 Covariant Quantities
3. 11.3 Gauged Spacetime Translations
4. Appendix 11A Manipulating Covariant Derivatives
4. 12 - Survey of Supergravities
1. 12.1 The Minimal Superalgebras
2. 12.2 The R-Symmetry Group
3. 12.3 Multiplets
4. 12.4 Supergravity Theories: Towards a Catalogue
5. 12.5 Scalars and Geometry
6. 12.6 Solutions and Preserved Supersymmetries
11. Part IV: Complex Geometry and Global SUSY
1. 13 - Complex Manifolds
1. 13.1 The Local Description of Complex and Kähler Manifolds
2. 13.2 Mathematical Structure of Kähler Manifolds
3. 13.3 The Kähler Manifolds CPn
4. 13.4 Symmetries of Kähler Metrics
2. 14 - General Actions with N = 1 Supersymmetry
1. 14.1 Multiplets
2. 14.2 Generalized Actions by Multiplet Calculus
3. 14.3 Kähler Geometry from Chiral Multiplets
4. 14.4 General Couplings of Chiral Multiplets and Gauge Multiplets
5. 14.5 The Physical Theory
6. Appendix 14A Superspace
7. Appendix 14B Appendix: Covariant Supersymmetry Transformations
12. Part V: Superconformal Construction of Supergravity Theories
1. 15 - Gravity as a Conformal Gauge Theory
2. 16 - The Conformal Approach to Pure N = 1 Supergravity
1. 16.1 Ingredients
2. 16.2 The action
3. 17 - Construction of the Matter-Coupled N = 1 Supergravity
1. 17.1 Superconformal Tensor Calculus
2. 17.2 Construction of the Action
3. 17.3 Projective Kähler Manifolds
4. 17.4 From Conformal to Poincaré Supergravity
5. 17.5 Review and Preview
6. Appendix 17A Kähler–Hodge Manifolds
7. Appendix 17B Steps in the Derivation of (17.7)
13. Part VI: N = 1 Supergravity Actions and Applications
1. 18 - The Physical N = 1 Matter-Coupled Supergravity
1. 18.1 The Physical Action
2. 18.2 Transformation Rules
3. 18.3 Further Remarks
2. 19 - Applications of N = 1 Supergravity
1. 19.1 Supersymmetry Breaking and the Super-BEH Effect
2. 19.2 The Gravity Mediation Scenario
3. 19.3 No-Scale models
4. 19.4 Supersymmetry and Anti-de Sitter Space
5. 19.5 R-symmetry and Fayet–Iliopoulos terms
14. Part VII: Extended N = 2 Supergravity
1. 20 - Construction of the Matter-Coupled N = 2 Supergravity
1. 20.1 Global Supersymmetry
2. 20.2 N = 2 Superconformal Calculus
3. 20.3 Special Geometry
4. 20.4 From Conformal to Poincaré Supergravity
5. Appendix 20A SU(2) Conventions and Triplets
6. Appendix 20B Dimensional Reduction 6 → 5 → 4
7. Appendix 20C Definition of Rigid Special Kähler Geometry
2. 21 - The Physical N = 2 Matter-Coupled Supergravity
1. 21.1 The Bosonic Sector
2. 21.2 The Symplectic Formulation
3. 21.3 Action and Transformation Laws
4. 21.4 Applications
5. 21.5 Remarks
15. Part VIII: Classical Solutions and the AdS/CFT Correspondence
1. 22 - Classical Solutions of Gravity and Supergravity
1. 22.1 Some Solutions of the Field Equations
2. 22.2 Killing Spinors and BPS Solutions
3. 22.3 Killing Spinors for Anti-de Sitter Space
4. 22.4 Extremal Reissner–Nordström Spacetimes as BPS Solutions
5. 22.5 The Black Hole Attractor Mechanism
6. 22.6 Supersymmetry of the Black Holes
7. 22.7 First Order Gradient Flow Equations
8. 22.8 The Attractor Mechanism – Fast and Furious
9. Appendix 22A Killing Spinors for pp-waves
2. 23 - The AdS/CFT Correspondence
1. 23.1 The N = 4 SYM Theory
2. 23.2 Type IIB String Theory and D3-Branes
3. 23.3 The D3-Brane Solution of Type IIB Supergravity
4. 23.4 Kaluza–Klein Analysis on AdS5 ⊗ S5
5. 23.5 Euclidean AdS and its Inversion Symmetry
6. 23.6 Inversion and CFT Correlation Functions
7. 23.7 The Free Massive Scalar Field in Euclidean AdSd+1
8. 23.8 AdS/CFT Correlators in a Toy Model
9. 23.9 Three-Point Correlation Functions
10. 23.10 Two-Point Correlation Functions
11. 23.11 Holographic Renormalization
12. 23.12 Holographic RG Flows