| Description |
1 online resource (ix, 130 pages) |
| Series |
SpringerBriefs in mathematical physics, 2197-1757 ; volume 1 |
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SpringerBriefs in mathematical physics ; v. 1.
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| Contents |
Preface; Contents; 1 Introduction; 1.1 Supergravity and Superstring; 1.2 Gravitational Field; 1.2.1 Metric Formulation; 1.2.2 Vielbein Formulation; 1.3 Yang -- Mills Field; 1.4 Antisymmetric Tensor Field; 1.4.1 Dual Field; 1.4.2 Self-dual Field; 1.4.3 Massive Chern -- Simons Type Theory; References; 2 Supergravities in Four Dimensions; 2.1 Superalgebras and Supermultiplets; 2.2 Supersymmetric Field Theories; 2.3 mathcalN=1 Poincaré Supergravity; 2.4 Local Supersymmetry of mathcalN=1 Poincaré Supergravity; 2.4.1 Invariance of the Action; 2.4.2 Commutator Algebra |
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2.5 mathcalN=1 Anti de Sitter Supergravity2.6 Extended Supersymmetries; 2.7 mathcalN=2 Poincaré Supergravity; 2.8 mathcalN=2 Anti de Sitter Supergravity; 2.9 mathcalN 3 Supergravities; References; 3 Superalgebras and Supermultiplets; 3.1 Spinors in General Dimensions; 3.1.1 Gamma Matrices; 3.1.2 Dirac Spinors; 3.1.3 Weyl Spinors; 3.1.4 Majorana Spinors; 3.1.5 Majorana -- Weyl Spinors; 3.1.6 Symplectic Majorana Spinors; 3.2 Super Poincaré Algebras; 3.3 Supermultiplets; 3.4 Massless Sectors of M Theory and Superstring Theory; 3.5 Super Anti de Sitter Algebras; References |
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4 Global Non-compact Symmetries4.1 Non-linear Sigma Models; 4.1.1 SL(2, mathbbR)/SO(2) Non-linear Sigma Model; 4.2 Duality Symmetry; 4.2.1 Duality Symmetry in General Even Dimensions; 4.2.2 Compact Duality Symmetry; 4.2.3 Non-compact Duality Symmetry; 4.3 D=4, mathcalN=8 Poincaré Supergravity; References; 5 Poincaré Supergravities in Higher Dimensions; 5.1 General Structure of Poincaré Supergravities; 5.2 D=11, mathcalN=1 Poincaré Supergravity; 5.3 D=10, mathcalN=(1,1) Poincaré Supergravity; 5.4 D=10, mathcalN=(2,0) Poincaré Supergravity; 5.5 D=10, mathcalN=(1,0) Poincaré Supergravity |
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7.1 Gauged Supergravities and Massive Supergravities7.2 D=4, mathscrN=8 Gauged Supergravity; 7.3 Gauged Supergravities in Higher Dimensions; 7.3.1 D=7, mathscrN=4 Gauged Supergravity; 7.3.2 D=5, mathscrN=8 Gauged Supergravity; 7.4 D=10, mathscrN=(1,1) Massive Supergravity; References; Appendix A Notation and Conventions; Appendix B Formulae of Gamma Matrices; Index |
| Summary |
This book is a pedagogical introduction to supergravity, a gravitational field theory that includes supersymmetry (symmetry between bosons and fermions) and is a generalization of Einstein's general relativity. Supergravity provides a low-energy effective theory of superstring theory, which has attracted much attention as a candidate for the unified theory of fundamental particles, and it is a useful tool for studying non-perturbative properties of superstring theory such as D-branes and string duality. This work considers classical supergravities in four and higher spacetime dimensions with their applications to superstring theory in mind. More concretely, it discusses classical Lagrangians (or field equations) and symmetry properties of supergravities. Besides local symmetries, supergravities often have global non-compact symmetries, which play a crucial role in their applications to superstring theory. One of the main features of this book is its detailed discussion of these non-compact symmetries. The aim of the book is twofold. One is to explain the basic ideas of supergravity to those who are not familiar with it. Toward that end, the discussions are made both pedagogical and concrete by stating equations explicitly. The other is to collect relevant formulae in one place so as to be useful for applications to string theory. The subjects discussed in this book include the vielbein formulation of gravity, supergravities in four dimensions, possible types of spinors in various dimensions, superalgebras and supermultiplets, non-linear sigma models for non-compact Lie groups, electric-magnetic duality symmetries, supergravities in higher dimensions, dimensional reductions, and gauged and massive supergravities |
| Bibliography |
Includes bibliographical references at the end of each chapters and index |
| Notes |
Online resource; title from PDF title page (SpringerLink, viewed July 14, 2014) |
| Subject |
Supergravity.
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SCIENCE -- Energy.
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SCIENCE -- Mechanics -- General.
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SCIENCE -- Physics -- General.
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Supergravity
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| Form |
Electronic book
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| ISBN |
9784431548287 |
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4431548289 |
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