Chern-Simons (Super) Gravity by Hassaine, Mokhtar -- Read -- Imperial Library of Trantor

Index

Cover page Title Copyright Preface Contents 1 The Quantum Gravity Puzzle

1.1 Renormalizability and the Triumph of Gauge Theory

1.1.1 Quantum field theory 1.1.2 Enter gravity

1.2 Minimal Coupling, Connections and Gauge Symmetry 1.3 Gauge Symmetry and General Coordinate Transformations

2 Geometry: General Overview

2.1 Metric and Affine Structures

2.1.1 Metric structure 2.1.2 Connection

2.2 Nonabelian Gauge Fields

3 First Order Gravitation Theory

3.1 The Equivalence Principle

3.1.1 The vielbein 3.1.2 The Lorentz connection 3.1.3 A tale of two covariant derivatives 3.1.4 Invariant tensors

3.2 Curvature and Torsion Two-Forms

3.2.1 Lorentz curvature 3.2.2 Torsion 3.2.3 Riemann and Lorentz curvatures 3.2.4 Building blocks

3.3 Gravity as a Gauge Theory

4 Gravity in Higher Dimensions

4.1 Lovelock Lagrangians 4.2 Dynamical Content

4.2.1 Field equations 4.2.2 First and second order theories

4.3 Torsional Series 4.4 Born-Infeld Lagrangians

5 Chern-Simons Gravities

5.1 Selecting Sensible Theories in Three Dimensions

5.1.1 Extending the Lorentz group 5.1.2 Local Poincaré (quasi-) invariance 5.1.3 Local (anti-)de Sitter symmetry 5.1.4 Three-dimensional zoo

5.2 More Dimensions

5.2.1 The lesson from D = 3 5.2.2 Lovelock-Chern-Simons theories 5.2.3 Locally Poincaré invariant theory

5.3 Torsional Chern-Simons Gravities

6 Additional Features of Chern-Simons Gravity

6.1 Lovelock-Chern-SimonsCoefficients 6.2 Stability of CS-Gravitation Theories 6.3 Degrees of Freedom 6.4 Summary of Gravity Actions 6.5 Finite Action and the Beauty of Gauge Invariance

7 Black Holes, Particles and Branes

7.1 Chern-Simons Black Holes

7.1.1 Three-dimensional black holes 7.1.2 Higher dimensional C-S black holes

7.2 Naked Singularities, Particles and Branes

7.2.1 The darker side of the 3D black holes 7.2.2 Spinning point particles 7.2.3 Charged point particles 7.2.4 (D − 3)-branes as conical defects in D dimensions

7.3 Chern-Simons Branes

7.3.1 The simplest CS branes 7.3.2 General CS branes

8 Supersymmetry and supergravity

8.1 Supersymmetry

8.1.1 Superalgebras 8.1.2 Supergravity

8.2 From Rigid Supersymmetry to Supergravity

8.2.1 Standard supergravity 8.2.2 AdS superalgebras

8.3 Fermionic Generators

8.3.1 Closing the algebra

9 Chern-Simons Supergravities

9.1 AdS CS Supergravity Actions

9.1.1 AdS3 supergravity as a CS action in D = 3 9.1.2 AdS5 supergravity as a CS action in D = 5 9.1.3 Eleven-dimensional AdS CS supergravity action for osp(32|1)

9.2 Poincaré CS Supergravity Actions

9.2.1 Poincaré CS supergravity with Majorana spinors

10 Inönü-Wigner Contractions and Its Extensions

10.1 Three-Dimensional Case

10.1.1 Case without torsion in the action 10.1.2 Case with torsion in the action

10.2 From osp(32|1) CS Sugra to CS Sugra for the M-Algebra

11 Unconventional Supersymmetries

11.1 Local Supersymmetry without Gravitini 11.2 Matter and Interaction Fields 11.3 Combining Matter and Interaction Fields

12 Concluding Remarks Bibliography Index

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